When I refer to an eigenspace corresponding to an eigenvalue, I am referring to the subspace of R^n consisting of the eigenvectors corresponding to the eigenvalue and also including the zero vector
No, the matrix P has to be invertible, in which case your equation would imply B=A. Perhaps you had a typo; we could have PB = AP with an invertible matrix P to show similarity.
And the biggest invariant of all...is the quality of these videos!
When you say eigenspace are you referring to the eigenvectors?
When I refer to an eigenspace corresponding to an eigenvalue, I am referring to the subspace of R^n consisting of the eigenvectors corresponding to the eigenvalue and also including the zero vector
@@WrathofMath Also known as, see other video!
Can you also use the formula BP=AP to show similarity for the 2 by 2 matrix
No, the matrix P has to be invertible, in which case your equation would imply B=A. Perhaps you had a typo; we could have PB = AP with an invertible matrix P to show similarity.
phew ... what a density of information.
Yeah, covered a lot in this one!
If I don't recall it wrongly, similarity can be viewed as an isomorphism?
Thanks for watching; and indeed! For example it would be an isomorphism on the multiplicative group of invertible nxn matrices.