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  • Nilpotent matrices

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  • Definition of nilpotent matrix
  • Definition of index of nilpotency
  • Every nilpotent matrix is similar to a sum of nilpotent Jordan blocks
  • A complex square matrix is nilpotent iff all its eigenvalues are zero
  • Commuting diagonalizable and nilpotent decomposition over the complex numbers
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  1. Every nilpotent matrix is similar to a sum of nilpotent Jordan blocks

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  • Every square matrix is similar to one in Jordan form.Close match
  • Nilpotent matricesClose match
  • Definition of Jordan formClose match
  • Definition of index of nilpotencyClose match
  • Definition of nilpotent matrixClose match
  • Similarity of matrices is an equivalence relationClose match
  • Commuting diagonalizable and nilpotent decomposition over the complex numbersClose match
  • Definition of similar matricesClose match
  • Similarity of matricesClose match
  • Block matricesClose match
  • Canonical forms of matricesClose match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • A complex square matrix is nilpotent iff all its eigenvalues are zeroClose match
  • Definition of nilpotent linear transformationRelated
  • Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.Related
  • Matrix diagonalizationRelated
  • Similar matrices have the same eigenvalues and the same characteristic polynomials.Related
  • A matrix of rank k is equivalent to a matrix with 1 in the first k diagonal entries and 0 elsewhere.Related
  • Two matrices of the same size are equivalent if and only if they have the same rank.Related
  • Equivalence theorem for nonsingular matrices: the matrix A row-reduces to the identity matrix.Related

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