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Eigendecomposition of a matrix and Orthogonal matrix

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

Difference between Eigendecomposition of a matrix and Orthogonal matrix

Eigendecomposition of a matrix vs. Orthogonal matrix

In linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. In linear algebra, an orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. where I is the identity matrix.

Similarities between Eigendecomposition of a matrix and Orthogonal matrix

Eigendecomposition of a matrix and Orthogonal matrix have 19 things in common (in Unionpedia): Condition number, Determinant, Diagonal matrix, Diagonalizable matrix, Eigenvalues and eigenvectors, Gaussian elimination, Householder transformation, Invertible matrix, Linear algebra, Matrix decomposition, Newton's method, Normal matrix, Numerical analysis, Orthogonality, Singular-value decomposition, Spectral theorem, Symmetric matrix, Unit vector, Unitary matrix.

Condition number

In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument.

Condition number and Eigendecomposition of a matrix · Condition number and Orthogonal matrix · See more »

Determinant

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

Determinant and Eigendecomposition of a matrix · Determinant and Orthogonal matrix · See more »

Diagonal matrix

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

Diagonal matrix and Eigendecomposition of a matrix · Diagonal matrix and Orthogonal matrix · See more »

Diagonalizable matrix

In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P−1AP is a diagonal matrix.

Diagonalizable matrix and Eigendecomposition of a matrix · Diagonalizable matrix and Orthogonal matrix · See more »

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.

Eigendecomposition of a matrix and Eigenvalues and eigenvectors · Eigenvalues and eigenvectors and Orthogonal matrix · See more »

Gaussian elimination

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.

Eigendecomposition of a matrix and Gaussian elimination · Gaussian elimination and Orthogonal matrix · See more »

Householder transformation

In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin.

Eigendecomposition of a matrix and Householder transformation · Householder transformation and Orthogonal matrix · See more »

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.

Eigendecomposition of a matrix and Invertible matrix · Invertible matrix and Orthogonal matrix · See more »

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.

Eigendecomposition of a matrix and Linear algebra · Linear algebra and Orthogonal matrix · See more »

Matrix decomposition

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices.

Eigendecomposition of a matrix and Matrix decomposition · Matrix decomposition and Orthogonal matrix · See more »

Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

Eigendecomposition of a matrix and Newton's method · Newton's method and Orthogonal matrix · See more »

Normal matrix

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

Eigendecomposition of a matrix and Normal matrix · Normal matrix and Orthogonal matrix · See more »

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

Eigendecomposition of a matrix and Numerical analysis · Numerical analysis and Orthogonal matrix · See more »

Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

Eigendecomposition of a matrix and Orthogonality · Orthogonal matrix and Orthogonality · See more »

Singular-value decomposition

In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix.

Eigendecomposition of a matrix and Singular-value decomposition · Orthogonal matrix and Singular-value decomposition · See more »

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).

Eigendecomposition of a matrix and Spectral theorem · Orthogonal matrix and Spectral theorem · See more »

Symmetric matrix

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

Eigendecomposition of a matrix and Symmetric matrix · Orthogonal matrix and Symmetric matrix · See more »

Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

Eigendecomposition of a matrix and Unit vector · Orthogonal matrix and Unit vector · See more »

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.

Eigendecomposition of a matrix and Unitary matrix · Orthogonal matrix and Unitary matrix · See more »

The list above answers the following questions

Eigendecomposition of a matrix and Orthogonal matrix Comparison

Eigendecomposition of a matrix has 69 relations, while Orthogonal matrix has 105. As they have in common 19, the Jaccard index is 10.92% = 19 / (69 + 105).

References

This article shows the relationship between Eigendecomposition of a matrix and Orthogonal matrix. To access each article from which the information was extracted, please visit:

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