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  • Similarity of matrices

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  • Definition of similar matrices
  • Definition of similarity transform
  • Similar matrices have the same eigenvalues and the same characteristic polynomials.
  • Every square matrix is similar to one in Jordan form.
  • Similarity of matrices is an equivalence relation
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  1. Every square matrix is similar to one in Jordan form.

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  • Definition of Jordan formClose match
  • Every nilpotent matrix is similar to a sum of nilpotent Jordan blocksClose match
  • Similarity of matrices is an equivalence relationClose match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Canonical forms of matricesClose match
  • Matrix diagonalizationClose match
  • Definition of similar matricesClose match
  • Definition of rational formClose match
  • Similarity of matricesClose match
  • A matrix of rank k is equivalent to a matrix with 1 in the first k diagonal entries and 0 elsewhere.Close match
  • Similar matrices have the same eigenvalues and the same characteristic polynomials.Close match
  • A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match
  • Definition of square matrixClose match
  • Symmetric matricesClose match
  • Definition of equivalent matricesClose match
  • Every matrix is row-equivalent to a matrix in reduced row echelon form.Close match
  • Matrix equivalenceClose match
  • Block matricesClose match
  • Every matrix has an eigenvalue over the complex numbers.Close match
  • Definition of similarity transformClose match

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