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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. Similar matrices have the same eigenvalues and the same characteristic polynomials.

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  • Definition of similar matricesClose match
  • Similarity of matrices is an equivalence relationClose match
  • Similarity of matricesClose match
  • A matrix and its transpose have the same eigenvalues/characteristic polynomial.Close match
  • Definition of equivalent matricesClose match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Definition of similarity transformClose match
  • Two matrices of the same size are equivalent if and only if they have the same rank.Close match
  • Every square matrix is similar to one in Jordan form.Close match
  • Matrix diagonalizationClose match
  • Equivalent matrices represent the same linear transformation with resect to appropriate bases.Close match
  • Definition of equality of matricesClose match
  • Eigenvectors with distinct eigenvalues are linearly independent.Close match
  • Equivalence theorem for nonsingular matrices: the determinant of A is nonzero.Close match
  • The characteristic polynomial applied to the matrix gives the 0 matrix.Close match
  • Equivalence theorem for nonsingular matrices: the columns of A are linearly independent.Close match
  • Matrix equivalenceClose match
  • A matrix with real entries has eigenvalues occurring in conjugate pairs.Close match
  • Equivalence theorem for nonsingular matrices: the matrix A has an inverse.Close match
  • Equivalence theorem for nonsingular matrices: the transpose of the matrix A has an inverse.Close match

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