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...
36 KB (5,464 words) - 05:34, 1 February 2025
In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...
34 KB (5,806 words) - 14:46, 17 February 2025
In mathematics, trace diagrams are a graphical means of performing computations in linear and multilinear algebra. They can be represented as (slightly...
9 KB (1,244 words) - 19:37, 2 October 2021
is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector...
5 KB (377 words) - 12:12, 30 October 2023
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...
23 KB (2,965 words) - 00:14, 1 September 2024
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...
4 KB (569 words) - 16:23, 15 November 2024
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...
42 KB (5,912 words) - 03:52, 30 November 2024
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 →...
9 KB (1,485 words) - 09:34, 2 November 2024
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...
8 KB (1,081 words) - 22:11, 19 October 2024
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...
12 KB (2,121 words) - 04:29, 2 December 2024
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...
10 KB (1,555 words) - 14:56, 19 March 2023
field). These elements are "special" in that they form an algebraic subvariety of the general linear group – they satisfy a polynomial equation (since the...
11 KB (1,481 words) - 01:34, 27 July 2024
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...
19 KB (3,038 words) - 20:42, 5 December 2024
Lockheed U-2 aircraft Technical Report, a type of ISO document Trace (linear algebra) Ton of refrigeration Total return Textus Receptus: Printed Greek...
3 KB (399 words) - 17:01, 2 November 2024
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...
11 KB (1,940 words) - 01:53, 27 December 2024
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...
55 KB (7,173 words) - 20:57, 3 December 2024
variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It...
139 KB (14,095 words) - 07:14, 17 February 2025
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...
67 KB (9,169 words) - 00:24, 17 February 2025
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...
18 KB (3,185 words) - 06:40, 13 February 2025
(u)\operatorname {ad} (v)),} where tr denotes the trace of a linear operator. Namely: a Lie algebra g {\displaystyle {\mathfrak {g}}} is semisimple if...
61 KB (10,462 words) - 14:37, 29 January 2025
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...
5 KB (688 words) - 18:44, 16 January 2025
Adjoint representation (redirect from Adjoint representation of a Lie algebra)
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...
21 KB (3,516 words) - 09:22, 26 August 2024
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...
108 KB (13,491 words) - 16:28, 3 February 2025
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...
28 KB (4,804 words) - 01:38, 25 January 2025
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...
41 KB (6,608 words) - 09:12, 17 December 2024
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...
102 KB (13,609 words) - 15:12, 17 February 2025
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...
52 KB (8,423 words) - 01:18, 2 February 2025
C*-algebra of complex square matrices with the positive elements being the positive-definite matrices. The trace function defined on this C*-algebra is...
8 KB (1,318 words) - 06:03, 28 April 2024
students studying mathematics. From the Preface: Linear algebra, topology, differential and algebraic geometry are the indispensable tools of the mathematician...
7 KB (910 words) - 16:04, 16 February 2024
transformation). Linear algebra is the branch of mathematics concerned with systems of linear equations. In Boolean algebra, a linear function is a function...
12 KB (1,634 words) - 17:33, 19 January 2025