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Matrix similarity and Skew-symmetric matrix

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

Difference between Matrix similarity and Skew-symmetric matrix

Matrix similarity vs. Skew-symmetric matrix

In linear algebra, two n-by-n matrices and are called similar if for some invertible n-by-n 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.

Similarities between Matrix similarity and Skew-symmetric matrix

Matrix similarity and Skew-symmetric matrix have 12 things in common (in Unionpedia): Basis (linear algebra), Complex number, Determinant, Diagonal matrix, Eigenvalues and eigenvectors, Invertible matrix, Linear algebra, Linear map, Normal matrix, Spectral theorem, Trace (linear algebra), Unitary matrix.

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.

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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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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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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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Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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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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Normal matrix

In mathematics, a complex square matrix is normal if where is the conjugate transpose of.

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Spectral theorem

In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).

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Trace (linear algebra)

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.

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Unitary matrix

In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.

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The list above answers the following questions

Matrix similarity and Skew-symmetric matrix Comparison

Matrix similarity has 36 relations, while Skew-symmetric matrix has 48. As they have in common 12, the Jaccard index is 14.29% = 12 / (36 + 48).

References

This article shows the relationship between Matrix similarity and Skew-symmetric matrix. To access each article from which the information was extracted, please visit:

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