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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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A matrix and its transpose have the same eigenvalues/characteristic polynomial.

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A matrix and its transpose have the same determinant.Close match
Eigenvalues agree and eigenvectors correspond through coordinatesClose match
Matrix transpose is an involution.Close match
Matrix adjoint is an involution.Close match
Similar matrices have the same eigenvalues and the same characteristic polynomials.Close match
Eigenvalues and operations on matricesClose match
Transpose and adjointClose match
A matrix with real entries has eigenvalues occurring in conjugate pairs.Close match
The transpose of a sum of matrices is the sum of the transposes.Close match
Definition of characteristic equation of a matrixClose match
Matrix transpose commutes with matrix inverse.Close match
The eigenvalues of the inverse of a nonsingular matrix are the reciprocals of the eigenvalues.Close match
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.Close match
The conjugate of the transpose is the transpose of the conjugate.Close match
Transpose commutes with scalar multiplication.Close match
Every matrix has an eigenvalue over the complex numbers.Close match
The eigenvalues of a power of a matrix are the power the eigenvalues.Close match
The characteristic polynomial applied to the matrix gives the 0 matrix.Close match
The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.Close match
Diagonalizability requires splitting and equality of geometric and algebraic multiplicitiesClose match

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