Matrices

Matrix consimilarity

In linear algebra, two n-by-n matrices A and B are called consimilar if for some invertible matrix , where denotes the elementwise complex conjugation. So for real matrices similar by some real matrix , consimilarity is the same as matrix similarity. Like ordinary similarity, consimilarity is an equivalence relation on the set of matrices, and it is reasonable to ask what properties it preserves. The theory of ordinary similarity arises as a result of studying linear transformations referred to different bases. Consimilarity arises as a result of studying antilinear transformations referred to different bases. A matrix is consimilar to itself, its complex conjugate, its transpose and its adjoint matrix. Every matrix is consimilar to a real matrix and to a Hermitian matrix. There is a standard form for the consimilarity class, analogous to the Jordan normal form. (Wikipedia).

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From playlist Introduction to Matrices and Matrix Operations

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What is a matrix? Free ebook http://tinyurl.com/EngMathYT

From playlist Intro to Matrices

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From playlist Matrices

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From playlist Matrices

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From playlist Chemistry 1P: Preparation for General Chemistry

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From playlist Eigenvalues

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From playlist Introducing linear algebra

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From playlist Matrices

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From playlist MATH2018 Engineering Mathematics 2D

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From playlist The Diagonalization of Matrices

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From playlist MIT Calculus Revisited: Multivariable Calculus

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From playlist Introduction to Matrices and Matrix Operations

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From playlist Talks and Tutorials

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From playlist Linear Algebra

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From playlist Matrix Equations

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From playlist Introduction to Matrices and Matrix Operations

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From playlist A first course in Linear Algebra - N J Wildberger

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From playlist Popular Questions

Related pages

Matrix similarity | Equivalence relation | Antilinear map | Jordan normal form | Transpose | Linear algebra | Matrix (mathematics) | Hermitian matrix