Introduction Matrices - Similar matrices, congruent matrices and symmetric matrices

4 important questions on Introduction Matrices - Similar matrices, congruent matrices and symmetric matrices

What can be said about the eigenvectors of A when there exists a matrix S such that S-1AS=diag(λ1,...,λn)?

That A has n linear independent eigenvectors

Whe are two matrices congruent?

When there exists a regular matrix S such that B=STAS

What two properties transfer when two matrices are congruent?

symmetric and difinite
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What can be said about matrix A if it is congruent with a diagonal matrix?

That A is symmetric

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