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Matrix (mathematics) and Trace (linear algebra)

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Matrix (mathematics) and Trace (linear algebra)

Matrix (mathematics) vs. Trace (linear algebra)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.

Similarities between Matrix (mathematics) and Trace (linear algebra)

Matrix (mathematics) and Trace (linear algebra) have 40 things in common (in Unionpedia): Associative algebra, Basis (linear algebra), Bilinear form, Characteristic polynomial, Complex number, Derivative, Determinant, Diagonal matrix, Dimension (vector space), Dot product, Dual space, Eigenvalues and eigenvectors, Group representation, Hadamard product (matrices), Hermitian matrix, Hilbert space, Identity matrix, Inner product space, Jordan normal form, Kronecker product, Linear map, Main diagonal, Matrix calculus, Matrix exponential, Matrix multiplication, Matrix norm, Positive-definite matrix, Rank (linear algebra), Real number, Representation theory, ..., Scalar (mathematics), Skew-symmetric matrix, Special linear group, Square matrix, Statistics, Superalgebra, Symmetric matrix, Transpose, Triangular matrix, Vector space. Expand index (10 more) »

Associative algebra

In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.

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Basis (linear algebra)

In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.

Basis (linear algebra) and Matrix (mathematics) · Basis (linear algebra) and Trace (linear algebra) · See more »

Bilinear form

In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.

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Characteristic polynomial

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

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.

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Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

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Dot product

In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.

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Dual space

In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.

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Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

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Group representation

In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.

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Hadamard product (matrices)

In mathematics, the Hadamard product (also known as the Schur product or the entrywise product) is a binary operation that takes two matrices of the same dimensions, and produces another matrix where each element i,j is the product of elements i,j of the original two matrices.

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Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.

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Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

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Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

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Inner product space

In linear algebra, an inner product space is a vector space with an additional structure called an inner product.

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Jordan normal form

In linear algebra, a Jordan normal form (often called Jordan canonical form) of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called a Jordan matrix, representing the operator with respect to some basis.

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Kronecker product

In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.

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Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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Main diagonal

In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, or major diagonal) of a matrix A is the collection of entries A_ where i.

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Matrix calculus

In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.

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Matrix exponential

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.

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Matrix multiplication

In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.

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Matrix norm

In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions).

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Positive-definite matrix

In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.

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Rank (linear algebra)

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Representation theory

Representation theory is a branch of mathematics that studies 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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Scalar (mathematics)

A scalar is an element of a field which is used to define a vector space.

Matrix (mathematics) and Scalar (mathematics) · Scalar (mathematics) and Trace (linear algebra) · See more »

Skew-symmetric matrix

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition In terms of the entries of the matrix, if aij denotes the entry in the and; i.e.,, then the skew-symmetric condition is For example, the following matrix is skew-symmetric: 0 & 2 & -1 \\ -2 & 0 & -4 \\ 1 & 4 & 0\end.

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Special linear group

In mathematics, the special linear group of degree n over a field F is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion.

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Square matrix

In mathematics, a square matrix is a matrix with the same number of rows and columns.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Superalgebra

In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra.

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Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

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Transpose

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).

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Triangular matrix

In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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The list above answers the following questions

Matrix (mathematics) and Trace (linear algebra) Comparison

Matrix (mathematics) has 352 relations, while Trace (linear algebra) has 91. As they have in common 40, the Jaccard index is 9.03% = 40 / (352 + 91).

References

This article shows the relationship between Matrix (mathematics) and Trace (linear algebra). To access each article from which the information was extracted, please visit:

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