In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...
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is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector...
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In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...
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In mathematics, trace diagrams are a graphical means of performing computations in linear and multilinear algebra. They can be represented as (slightly...
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fetch Trace (linear algebra), the sum of the elements on the main diagonal of a square matrix or a linear transformation Field trace, a particular trace in...
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Lie algebra of SL(n, F) consists of all n×n matrices over F with vanishing trace. The Lie bracket is given by the commutator. The special linear group...
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Dimension (vector space) (redirect from Linear algebra/Dimension of a vector space)
a notion of dimension when one has a trace but no natural sense of basis. For example, one may have an algebra A {\displaystyle A} with maps η : K →...
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special cases states and traces are discussed in detail in (Takesaki 1979). A weight ω on a von Neumann algebra is a linear map from the set of positive...
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Matrix similarity (redirect from Similar (linear algebra))
In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that B = P − 1 A P . {\displaystyle...
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K-linear transformation of this vector space into itself. The trace, TrL/K(α), is defined as the trace (in the linear algebra sense) of this linear transformation...
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In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar-valued function on operators...
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field). These elements are "special" in that they form an algebraic subvariety of the general linear group – they satisfy a polynomial equation (since the...
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Lockheed U-2 aircraft Technical Report, a type of ISO document Trace (linear algebra) Ton of refrigeration Total return Textus Receptus: Printed Greek...
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variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It...
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Characteristic polynomial (category Linear algebra)
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...
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coefficients), M ↦ tr(AM) where A is the matrix of the coefficients; see Trace (linear algebra)#Inner product. A random orthogonal matrix is said to be distributed...
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Representation theory (redirect from Linear representation)
abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures...
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In mathematics, the special linear Lie algebra of order n {\displaystyle n} over a field F {\displaystyle F} , denoted s l n F {\displaystyle {\mathfrak...
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used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra. All trace-class operators are...
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software update Stack pointer Stored procedure Synthetic programming Trace (linear algebra), or "Spur" (German), of a square matrix Sp(n) and Sp(2n,F), a symplectic...
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transformation). Linear algebra is the branch of mathematics concerned with systems of linear equations. In Boolean algebra, a linear function is a function...
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(u)\operatorname {ad} (v)),} where tr denotes the trace of a linear operator. Namely: a Lie algebra g {\displaystyle {\mathfrak {g}}} is semisimple if...
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In mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...
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Eigenvalues and eigenvectors (redirect from Algebraic multiplicity)
In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear...
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Matrix (mathematics) (section Trace)
article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square...
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Matrix norm (redirect from Trace norm)
Applied Numerical Linear Algebra, section 1.7, published by SIAM, 1997. Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, published by SIAM...
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C*-algebra of complex square matrices with the positive elements being the positive-definite matrices. The trace function defined on this C*-algebra is...
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Matrix multiplication (category Numerical linear algebra)
In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication...
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Appendix:Glossary of abstract algebra in Wiktionary, the free dictionary. Abstract algebra is the subject area of mathematics that studies algebraic structures, such...
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(Terse) Introduction to Linear Algebra, American Mathematical Society, ISBN 978-0-8218-4419-9 Lax, Peter (1996), Linear algebra, Wiley-Interscience,...
34 KB (5,967 words) - 23:34, 15 June 2024