Matrices

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 i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: or in matrix form: Hermitian matrices can be understood as the complex extension of real symmetric matrices. If the conjugate transpose of a matrix is denoted by , then the Hermitian property can be written concisely as Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are , although note that in quantum mechanics, typically means the complex conjugate only, and not the conjugate transpose. (Wikipedia).

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From playlist Course 4: Linear Algebra (Fall 2017)

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From playlist Mathematics (All Of It)

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My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.

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This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.

From playlist Linear Algebra

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Commutator | Gell-Mann matrices | If and only if | Vector space | Pauli matrices | Self-adjoint operator | Diagonalizable matrix | Spectral theorem | Orthogonal basis | Main diagonal | Dot product | Skew-Hermitian matrix | Imaginary number | Conjugate transpose | Imaginary unit | Spin (physics) | Mathematics | Square matrix | Real number | Symmetric matrix | Unitary matrix | Complex conjugate | Eigenvalues and eigenvectors | Complex number | Charles Hermite | Matrix multiplication | Hermitian adjoint | Eigendecomposition of a matrix | Haynsworth inertia additivity formula