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...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

In mathematics, trace diagrams are a graphical means of performing computations in linear and multilinear algebra. They can be represented as (slightly...

is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector...

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...

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...

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...

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 →...

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...

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...

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...

field). These elements are "special" in that they form an algebraic subvariety of the general linear group – they satisfy a polynomial equation (since the...

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...

Lockheed U-2 aircraft Technical Report, a type of ISO document Trace (linear algebra) Ton of refrigeration Total return Textus Receptus: Printed Greek...

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...

abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures...

variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It...

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...

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...

(u)\operatorname {ad} (v)),} where tr denotes the trace of a linear operator. Namely: a Lie algebra g {\displaystyle {\mathfrak {g}}} is semisimple if...

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...

way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is...

article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square...

Applied Numerical Linear Algebra, section 1.7, published by SIAM, 1997. Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, published by SIAM...

In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication...

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...

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...

C*-algebra of complex square matrices with the positive elements being the positive-definite matrices. The trace function defined on this C*-algebra is...

students studying mathematics. From the Preface: Linear algebra, topology, differential and algebraic geometry are the indispensable tools of the mathematician...

transformation). Linear algebra is the branch of mathematics concerned with systems of linear equations. In Boolean algebra, a linear function is a function...