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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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Definition of index of nilpotency

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Definition of nilpotent matrixClose match
Nilpotent matricesClose match
Every nilpotent matrix is similar to a sum of nilpotent Jordan blocksClose match
A complex square matrix is nilpotent iff all its eigenvalues are zeroClose match
Definition of nilpotent linear transformationClose match
Definition of nullity of a matrixClose match
Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.Close match
Rank and nullityRelated
Commuting diagonalizable and nilpotent decomposition over the complex numbersRelated
Definition of 0 matrixRelated
Equivalence theorem for nonsingular matrices: the matrix A has rank n.Related
Definition of nonsingular matrix: matrix is invertibleRelated
Equivalence theorem for nonsingular matrices: the dimension of the column space of A is n.Related
Equivalence theorem for nonsingular matrices: the matrix A has an inverse.Related
Rank–nullity theorem for an m-by-n matrixRelated
Equivalence theorem for nonsingular matrices: the matrix A does not have 0 as an eigenvalue.Related
Nonsingular matrices and equivalencesRelated
Equivalence theorem for nonsingular matrices: the matrix A row-reduces to the identity matrix.Related
Definition of identity matrixRelated
Condition number measures relative sensitivityRelated

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