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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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Definition of similarity transform

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Similarity of matricesClose match
Definition of similar matricesClose match
Similarity of matrices is an equivalence relationClose match
Definition of equivalent matricesClose match
Similar matrices have the same eigenvalues and the same characteristic polynomials.Close match
Equivalent matrices represent the same linear transformation with resect to appropriate bases.Close match
Matrix equivalenceClose match
Every square matrix is similar to one in Jordan form.Close match
Equivalence theorem for nonsingular matrices: the matrix A is a change-of-basis matrix.Close match
Matrix diagonalizationRelated
Every complex square matrix is unitarily similar to an upper triangular matrixRelated
InverseRelated
Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is an isomorphism.Related
Symmetric matricesRelated
Definition of identity matrixRelated
Definition of permutation matrixRelated
Equivalence theorem for nonsingular matrices: the transpose of the matrix A has an inverse.Related
Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax has an inverse.Related
ConjugationRelated
Transpose and adjointRelated

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