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In operator algebras, the Toeplitz algebra is the C*-algebra generated by the unilateral shift on the Hilbert space l2(N). Identifying l2(N) with the Hardy
Toeplitz_algebra
German mathematician (1881–1940)
(1st edition, 1963) Calderón–Toeplitz operator Silverman–Toeplitz theorem Hellinger–Toeplitz theorem Toeplitz algebra Toeplitz matrix Inscribed square problem
Otto_Toeplitz
Matrix with shifting rows
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to
Toeplitz_matrix
function in C(T). The algebra C*(S) is called the Toeplitz algebra. Theorem (Coburn) C*(V) is isomorphic to the Toeplitz algebra and V is the isomorphic
Wold's_decomposition
Mathematical objects that generalise the notion of Hilbert spaces
A} . The Toeplitz algebra T ( E ) {\displaystyle {\mathcal {T}}(E)} is the universal Toeplitz representation. That is, there is a Toeplitz representation
Hilbert_C*-module
Topics referred to by the same term
diagonals Toeplitz operator, the compression of a multiplication operator on the circle to the Hardy space Toeplitz algebra, the C*-algebra generated
Toeplitz
(link) Böttcher, Albrecht; Grudsky, Sergei M. (2000), Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis, Birkhäuser, ISBN 978-3-0348-8395-5
Toeplitz_operator
calculus shows that the C*-algebra generated by T is Mn(C*(Tz)), where C*(Tz) denotes the Toeplitz algebra, the C*-algebra generated by the unilateral
Bunce–Deddens_algebra
Hessenberg matrix Hessian matrix Vandermonde matrix Stochastic matrix Toeplitz matrix Circulant matrix Hankel matrix (0,1)-matrix Bohemian matrices Matrix
Outline_of_linear_algebra
Number raised to the third power
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a
Cube_(algebra)
Rotation of a circle by an angle of π times an irrational number
not uniquely ergodic." Bernoulli map Modular arithmetic Siegel disc Toeplitz algebra Phase locking (circle map) Weyl sequence Fisher, Todd (2007). "Circle
Irrational_rotation
graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz algebras and Cuntz-Krieger
Graph_C*-algebra
notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of data structures
List_of_theorems
Matrix defined using smaller matrices called blocks
block Toeplitz matrix is another special block matrix, which contains blocks that are repeated down the diagonals of the matrix, as a Toeplitz matrix
Block_matrix
Linear algebra matrix
to the right relative to the preceding row. It is a particular kind of Toeplitz matrix. In numerical analysis, circulant matrices are important because
Circulant_matrix
Irish mathematician (1948–2006)
C*-algebras, the spectral and index theory of Toeplitz operators on Hardy spaces of ordered groups and bounded symmetric domains, and the C*-algebra approach
Gerard_Murphy_(mathematician)
Russian mathematician
Moscow State University since 2004. He defended the thesis "Matrices of the Toeplitz type and their applications" for the degree of Doctor of Physical and Mathematical
Evgeny_Tyrtyshnikov
Several equations of degree 1 to be solved simultaneously
three equations valid. Linear systems are a fundamental part of linear algebra, a subject used in most modern mathematics. Computational algorithms for
System_of_linear_equations
Matrix equal to its transpose
Sylvester's law of inertia Toeplitz matrix Transpositions matrix See also symmetry in mathematics. Jesús Rojo García (1986). Álgebra lineal (in Spanish) (2nd ed
Symmetric_matrix
Mathematical study of linear operators
collection of operators forms an algebra over a field, then it is an operator algebra. The description of operator algebras is part of operator theory. Single
Operator_theory
Special kind of square matrix
algebra, denoted n . {\displaystyle {\mathfrak {n}}.} This algebra is the derived Lie algebra of b {\displaystyle {\mathfrak {b}}} , the Lie algebra of
Triangular_matrix
Type of vector space in math
Nishio, Masaharu; Tanaka, Kiyoki (2017), "Harmonic Bergman kernels and Toeplitz operators on the ball with radial measures", Rev. Roumaine Math. Pures
Hilbert_space
Vector satisfying some of the criteria of an eigenvector
In linear algebra, a generalized eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria
Generalized_eigenvector
Matrix whose only nonzero elements are on its main diagonal
Jordan normal form Multiplication operator Tridiagonal matrix Toeplitz matrix Toral Lie algebra Circulant matrix Proof: given the elementary matrix e i j
Diagonal_matrix
Used to count, measure, and label
printed". American Antiquity. 28 (2): 256. doi:10.2307/278400. JSTOR 278400. Toeplitz, Otto (2024). The Calculus: A Genetic Approach. University of Chicago Press
Number
mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Determinant of large Toeplitz matrices
theorems describe the asymptotic behaviour of the determinants of large Toeplitz matrices. They were first proved by Gábor Szegő. Let w {\displaystyle w}
Szegő_limit_theorems
Recursive algorighm in linear algebra
recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix. The algorithm runs in Θ(n2)
Levinson_recursion
Hessenberg matrices, on updating the QR factorization, superfast solution of Toeplitz systems, parallel algorithms for solving eigenvalue problems, as well as
William_B._Gragg
Matrix with nonzero elements on the main diagonal and the diagonals above and below it
; Reichel, L. (2013). "Tridiagonal Toeplitz matrices: Properties and novel applications". Numerical Linear Algebra with Applications. 20 (2): 302. doi:10
Tridiagonal_matrix
space Fundamental theorem of Hilbert spaces Gram–Schmidt process Hellinger–Toeplitz theorem Hilbert space Inner product space Legendre polynomials Matrices
List of functional analysis topics
List_of_functional_analysis_topics
Russian mathematician
His Ph.D. thesis, dealing with geometric aspects of Hankel operators and Toeplitz operators, was supervised by Nikolai Kapitonovich Nikolski. From 1986 to
Sergei_Treil
(1884–1944) Maxime Bôcher (1867–1918) Leonard Eugene Dickson (1874–1954), algebra and number theory Jesse Douglas (1897–1965), Fields Medalist Edward Kasner
List of mathematicians born in the 19th century
List_of_mathematicians_born_in_the_19th_century
Mathematical group of loops in a Lie group
to affine Kac–Moody algebras, conformal field theory, and the Verlinde formula. In algebraic geometry one also studies algebraic loop groups, defined
Loop_group
Böttcher, Albrecht; Silbermann, Bernd (1999). Introduction to Large Truncated Toeplitz Matrices. Springer New York. p. 70. doi:10.1007/978-1-4612-1426-7_3.
Pseudospectrum
relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be viewed as a particular type of positive-definite kernel
Positive-definite function on a group
Positive-definite_function_on_a_group
German mathematician (1908 – 1975)
Courant, Erich Bessel-Hagen, Felix Hausdorff, and the joint Hausdorff–Otto Toeplitz seminar. He graduated summa cum laude in 1930 with a thesis about countable
Helmut_Ulm
Matrix symmetric about its center
{\displaystyle {\begin{bmatrix}a&b&c\\d&e&d\\c&b&a\end{bmatrix}}.} Symmetric Toeplitz matrices are centrosymmetric. If A and B are n × n centrosymmetric matrices
Centrosymmetric_matrix
Square matrix in which each ascending skew-diagonal from left to right is constant
In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a rectangular matrix in which each ascending skew-diagonal
Hankel_matrix
Integral expressing the amount of overlap of one function as it is shifted over another
Scaled correlation Titchmarsh convolution theorem Toeplitz matrix (convolutions can be considered a Toeplitz matrix operation where each row is a shifted copy
Convolution
Russian mathematician (1937–2023)
factoring algorithm" (PDF). Numdam. Bourbaki Seminar. 1999. Rademacher, Hans; Toeplitz, Otto (2002). Von Zahlen und Figuren [From Numbers and Figures] (in German)
Yuri_Manin
German mathematician
quantisation, e.g. Berezin-Toeplitz-Quantisierung and infinite dimensional Lie algebras of geometric origin, like the algebras of Krichever- Novikov type
Martin_Schlichenmaier
Aspect of a numerical matrix
In the mathematical field of linear algebra and convex analysis, the numerical range or field of values or Wertvorrat or Wertevorrat of a complex n ×
Numerical_range
Set of matrices
they may be Toeplitz matrices or upper Hessenberg matrices. Bohemian matrices are used in software testing, particularly in linear algebra applications
Bohemian_matrices
Method for matrix characteristic polynomials
It computes this coefficients vector recursively as the product of a Toeplitz matrix and the coefficients vector an ( n − 1 ) × ( n − 1 ) {\displaystyle
Samuelson–Berkowitz_algorithm
In mathematics, a linear operator acting on inner product space
In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting
Positive_operator
German mathematician and chess player
August 1842 – 6 January 1922) was a German mathematician who worked on algebraic geometry and invariant theory. He was also a chess master. Rosanes was
Jakob_Rosanes
Matrix with non-zero elements only in a diagonal band
obtains a lower triangular matrix. Upper and lower Hessenberg matrices Toeplitz matrices when bandwidth is limited. Block diagonal matrices Shift matrices
Band_matrix
Taussky (1906–1995), algebraic number theory and algebra Olry Terquem (1782–1862), mathematician Otto Toeplitz (1881–1940), linear algebra and functional analysis
List_of_Jewish_mathematicians
Mathematical algorithm
calculation of the inverse matrix. For non-structured matrices (not sparse, not Toeplitz,...) this requires O ( n 3 ) {\displaystyle O(n^{3})} operations. The method
Inverse_iteration
Matrix class
though all algorithms can be easily generalized to rectangular matrices). Toeplitz matrix Fay's trisecant identity Bostan, A.; Jeannerod, C.-P.; Schost, É
Cauchy_matrix
that it is impossible to make a one-to-one mapping between them and the algebraic numbers. In other words, the cardinality of the set of transcendentals
List_of_conjectures
Representation theory of the symplectic group
an infinitesimal level the semigroup is described by a cone in the Lie algebra of SU(1,1) that can be identified with a light cone. The same framework
Oscillator_representation
Matrix equal to its conjugate-transpose
B={\tfrac {1}{2}}{\left(C-C^{\mathsf {H}}\right)}.} This is known as the Toeplitz decomposition of C {\displaystyle C} . For a complex matrix M {\displaystyle
Hermitian_matrix
iteratively Gaussian elimination Levinson recursion: solves equation involving a Toeplitz matrix Stone's method: also known as the strongly implicit procedure or
List_of_algorithms
Russian mathematician
until his late eighties. His work was mainly, but not exclusively, in algebra and number theory, and he had a great interest in numerical methods as
Alexander_Ostrowski
Class of numerical techniques
equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently, and this, along
Finite_difference_method
Image reconstruction algorithms
data problems: Applications to estimating point-process intensites and toeplitz constrained covariance estimates". Proceedings of the IEEE. 5 (7): 3223–3227
Iterative_reconstruction
more general setting originally studied by Wiener while others have used Toeplitz matrix advances to speed up factor calculations. Consider the n × n {\displaystyle
Polynomial matrix spectral factorization
Polynomial_matrix_spectral_factorization
Square of a triangular number
also be proved easily (but uninformatively) by induction, and states that Toeplitz (1963) provides "an interesting old Arabic proof". Kanim (2004) provides
Squared_triangular_number
South Korean mathematician (born 1966)
Meng (2021). "Structured perturbation analysis for an infinite size quasi-Toeplitz matrix equation with applications". BIT Numerical Mathematics. 61 (3):
Kim_Hyun-Min
Swedish American mathematician (1923–2016)
The Harald Cramér Volume. Wiley. Szegő, Gábor; Grenander, Ulf (1958). Toeplitz forms and their applications. Chelsea. Grenander, Ulf; Rosenblatt, M (1957)
Ulf_Grenander
Austrian mathematician (1905–1989)
recommendation of Emmy Noether, he was appointed an assistant of Otto Toeplitz in Bonn University in 1929–1930. During this time he began transition to
Gottfried_Köthe
German–British physicist (1882–1970)
Göttingen and do his habilitation there. Born accepted. Toeplitz helped him brush up on his matrix algebra so he could work with the four-dimensional Minkowski
Max_Born
Trying to map moments to a measure that generates them
trigonometric moment problem in which the Hankel matrices are replaced by Toeplitz matrices and the support of μ is the complex unit circle instead of the
Moment_problem
Russian mathematician (born 1940)
spaces, Sobolev embeddings and optimal sign transport". Algebra i Analiz. 34 (2): 118–151. (I) Toeplitz matrices and operators, Cambridge Studies in Advanced
Nikolai_Kapitonovich_Nikolski
Problem book in mathematical analysis
eminent mathematicians (Bernays, Courant, Fejér, E. Landau, F. Riesz, Toeplitz) had read over the galley proofs while the work was in press and its early
Problems and Theorems in Analysis
Problems_and_Theorems_in_Analysis
Infinite sum
results concerning possible summability methods are known. The Silverman–Toeplitz theorem characterizes matrix summation methods, which are methods for summing
Series_(mathematics)
Mathematics term
ISBN 978-0-521-18071-9. Zbl 1221.68183. Cassaigne, Julien; Karhumäki, Juhani (1997). "Toeplitz words, generalized periodicity and periodically iterated morphisms". European
Morphic_word
On decimal expansions of fractions with prime denominator and even repeat period
Bassam Abdul-Baki, Extended Midy's Theorem, 2005. Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur
Midy's_theorem
Property of a mathematical matrix
{\displaystyle A\mathbf {x} .} If M {\displaystyle M} is a symmetric Toeplitz matrix, i.e. the entries m i j {\displaystyle m_{ij}} are given as a function
Definite_matrix
Russian physicist and mathematician
entanglement entropy of the XX (isotropic) and XY Heisenberg models. He used Toeplitz Determinants and Fisher-Hartwig Formula for the calculation. In the Valence-Bond-Solid
Vladimir_Korepin
Reconstruction of a filtered signal
deconvolve the data. However, by formulating the problem as the solution of a Toeplitz matrix and using Levinson recursion, we can relatively quickly estimate
Deconvolution
American mathematician (1932–2021)
of AW*-algebras advised by Irving Kaplansky (1955). He taught mathematics at Cornell University (1955–68) where he started his work on Toeplitz and Wiener-Hopf
Harold_Widom
Functional analysis concept
{\displaystyle C^{\ast }} -algebra of L ( H ) {\displaystyle L(H)} modulo the compact operators is called the Calkin algebra, in which one can consider
Compact operator on Hilbert space
Compact_operator_on_Hilbert_space
Part of Fredholm theories in integral equations
does not vanish on T {\displaystyle \mathbf {T} } , and let Tφ denote the Toeplitz operator with symbol φ, equal to multiplication by φ followed by the orthogonal
Fredholm_operator
Linear operator defined on a dense linear subspace
bounded operators, unbounded operators on a given space do not form an algebra, nor even a linear space, because each one is defined on its own domain
Unbounded_operator
Operator on a Hilbert space that shifts basis vectors
\\0&0&1&0&\cdots \\\vdots &\vdots &\vdots &\vdots &\ddots \end{bmatrix}}} This is a Toeplitz operator whose symbol is the function f ( z ) = z {\displaystyle f(z)=z}
Unilateral_shift_operator
Soviet-Israeli-American mathematician
1090/S0002-9947-1993-1118827-0. with Kehe Zhu: "An application of Tauberian theorems to Toeplitz operators." Journal of Operator Theory, 1995, 353–361. JSTOR 24714916 with
Boris_Korenblum
Infinite series that is not convergent
\lim _{\alpha \to 0^{+}}\sum _{n}c_{n}e^{-\alpha n^{2}}=s.} Silverman–Toeplitz theorem Abel–Dini–Pringsheim theorem "Summation methods". Michon's Numericana
Divergent_series
American mathematician (1933–2017)
spaces H ( b ) {\displaystyle {\mathcal {H}}(b)} and the ranges of certain Toeplitz operators. Using reproducing kernel Hilbert space techniques, he gave elegant
Donald_Sarason
Discrete Fourier transform algorithm
polynomial multiplication, efficient matrix–vector multiplication for Toeplitz, circulant and other structured matrices, filtering algorithms (see overlap–add
Fast_Fourier_transform
American mathematician (1932–2007)
Fischer, D.; Golub, G.; Hald, O.; Leiva, C.; Widlund, O. (1974). "On Fourier-Toeplitz methods for separable elliptic problems". Mathematics of Computation. 28
Gene_H._Golub
geometric terms used in invariant theory see the glossary of classical algebraic geometry. Definitions of many terms used in invariant theory can be found
Glossary_of_invariant_theory
Complex-valued function
is a group because The set of trace-class operators is an ideal in the algebra of bounded linear operators, so ( I + T ) ( I + T ′ ) − I = T + T ′ + T
Fredholm_determinant
Canadian-American mathematician (1921–2017)
ISSN 0002-9947. ——; Zeller, Karl (1963). "A biorthogonal system which is not a Toeplitz basis". Bulletin of the American Mathematical Society. 69 (5): 725–726
Albert_Wilansky
American mathematician
Mathematische Zeitschrift, 233(1), pp. 1–18. Bump, D., & Diaconis, P. (2002). "Toeplitz minors". Journal of Combinatorial Theory, Series A, 97(2), pp. 252–271
Daniel_Bump
Shape with same width in all directions
University of Chicago Press. pp. 212–221. ISBN 0-226-28256-2. Rademacher, Hans; Toeplitz, Otto (1957). "Chapter 25: Curves of Constant Breadth". The Enjoyment of
Curve_of_constant_width
encyclopediaofmath.org. Retrieved 2020-09-07. Hogben, Leslie (2006), Handbook of Linear Algebra (Discrete Mathematics and Its Applications), Boca Raton: Chapman & Hall/CRC
List_of_named_matrices
the resulting sum has some generalized kind of second derivative using Toeplitz operators. Later on, Georg Cantor generalized Riemann's techniques to show
Set_of_uniqueness
Graduate-level textbooks in mathematics
Volume Title Author(s) Publication Date Pages ISBN/LCCN 1 Algebraic Theory of Numbers Hermann Weyl 1940 223 LCCN 40-13494 2 Convergence and Uniformity
Annals_of_Mathematics_Studies
Linear operator equal to its own adjoint
A:\operatorname {Dom} (A)\to H} a symmetric operator. According to Hellinger–Toeplitz theorem, if Dom ( A ) = H {\displaystyle \operatorname {Dom} (A)=H} then
Self-adjoint_operator
Estimation method that minimizes the mean square error
Levinson recursion is a fast method when C Y {\displaystyle C_{Y}} is also a Toeplitz matrix. This can happen when y {\displaystyle y} is a wide sense stationary
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Canadian mathematician
Timotin, Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators, J. Funct. Anal., 259(10):2673-2701,2010. B. Aaranov, E. Fricain
Javad_Mashreghi
Public university in Bonn, Germany
Petri net, the Schönhage–Strassen algorithm, Faltings' theorem and the Toeplitz matrix are all named after University of Bonn mathematicians. University
University_of_Bonn
symmetric matrices, based on graph partitioning Levinson recursion — for Toeplitz matrices SPIKE algorithm — hybrid parallel solver for narrow-banded matrices
List of numerical analysis topics
List_of_numerical_analysis_topics
Russian-French mathematician
him the book The Enjoyment of Mathematics by Hans Rademacher and Otto Toeplitz, a book that piqued his curiosity and had a great influence on him. Gromov
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Aspect of mathematical spectrum theory
is closed. If T {\displaystyle T} is bounded and either hypernormal or Toeplitz, then σ e s s , 4 ( T ) = σ e s s , 5 ( T ) {\displaystyle \sigma _{\mathrm
Essential_spectrum
German mathematician (1868–1942)
Hausdorff was friends and colleagues with Eduard Study, and later with Otto Toeplitz, who were both outstanding mathematicians. After the takeover by the National
Felix_Hausdorff
Strasburger (1844–1912), Botany Heinrich von Sybel (1817–1895), History Otto Toeplitz (1881–1940), Mathematics Carl Troll (1899–1975), Geography Hermann Karl
List of University of Bonn people
List_of_University_of_Bonn_people
TOEPLITZ ALGEBRA
TOEPLITZ ALGEBRA
TOEPLITZ ALGEBRA
TOEPLITZ ALGEBRA
Boy/Male
Anglo, British, English
From the Oak Tree Meadow
Girl/Female
Muslim/Islamic
Great
Boy/Male
Muslim Egyptian
Servant (domestic). Small slave.
Female
English
 Pet form of English Ulrica, ULA means "wolf power." Compare with other forms of Ula.
Girl/Female
Danish, French, Indian, Latin, Traditional
Beautiful; Compound of 'Horse' and 'Snake'; Pretty Rose
Boy/Male
Hindu
Boy/Male
Muslim
Intelligent, Sagacious
Girl/Female
Arabic
Flower
Girl/Female
Indian
Virtuous, Honest, Excellent
Boy/Male
Muslim/Islamic
A nabee was named by this name
TOEPLITZ ALGEBRA
TOEPLITZ ALGEBRA
TOEPLITZ ALGEBRA
TOEPLITZ ALGEBRA
TOEPLITZ ALGEBRA
v. t.
To perform by algebra; to reduce to algebraic form.
n.
Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
n.
Either of the two parts of an algebraic equation, connected by the sign of equality.
n.
An algebraic curve, so called from its resemblance to a heart.
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
n.
That branch of algebra which treats of quadratic equations.
n.
The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
n.
Any particular system of characters, symbols, or abbreviated expressions used in art or science, to express briefly technical facts, quantities, etc. Esp., the system of figures, letters, and signs used in arithmetic and algebra to express number, quantity, or operations.
a.
Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings.
a.
That may be sqyared, or reduced to an equivalent square; -- said of a surface when the area limited by a curve can be exactly found, and expressed in a finite number of algebraic terms.
a.
A branch of algebra which relates to the direct search for unknown quantities.
n.
A homogeneous algebraic function of two or more variables, in general containing only positive integral powers of the variables, and called quadric, cubic, quartic, etc., according as it is of the second, third, fourth, fifth, or a higher degree. These are further called binary, ternary, quaternary, etc., according as they contain two, three, four, or more variables; thus, the quantic / is a binary cubic.
n.
One versed in algebra.
n.
A single algebraic expression; that is, an expression unconnected with any other by the sign of addition, substraction, equality, or inequality.
a.
That can be passed over in a single course; -- said of a curve when the coordinates of the point on the curve can be expressed as rational algebraic functions of a single parameter /.
a.
Susceptible of being solved; as, a soluble algebraic problem; susceptible of being disentangled, unraveled, or explained; as, the mystery is perhaps soluble.
a.
Alt. of Algebraical
v. t.
To change, as an algebraic expression or geometrical figure, into another from without altering its value.
n.
One of the terms in an algebraic expression.
adv.
By algebraic process.