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Eigenvalues and operations on matrices

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The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.
The eigenvalues of a power of a matrix are the power the eigenvalues.
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.
The eigenvalues of the inverse of a nonsingular matrix are the reciprocals of the eigenvalues.
A matrix and its transpose have the same eigenvalues/characteristic polynomial.

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The eigenvalues of the inverse of a nonsingular matrix are the reciprocals of the eigenvalues.

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The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.Close match
Eigenvalues and operations on matricesClose match
The eigenvalues of a power of a matrix are the power the eigenvalues.Close match
InverseClose match
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.Close match
Definition of eigenvector of a matrixClose match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Matrix inverse is an involution.Close match
Definition of eigenvalue of a matrixClose match
Equivalence theorem for nonsingular matrices: the matrix A has an inverse.Close match
Matrix transpose commutes with matrix inverse.Close match
Eigenvalues and eigenvectorsClose match
An eigenspace of a matrix is the null space of a related matrix.Close match
A matrix and its transpose have the same eigenvalues/characteristic polynomial.Close match
The inverse of a scalar multiple is the reciprocal times the inverse.Close match
The inverse of a matrix can be used to solve a linear system.Close match
The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.Close match
Matrix inverses are unique: if A and B are square matricesClose match
Definition of invertible matrixClose match
The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.Close match

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