If $A$ be a non singular matrix then what good does it do by constructing another matrix, say $P$ whose columns are a basis that consists of eigenvectors of $A$? Does it have something to do with thee eigenvectors of $A$ being a set of basis for the transformation. Also, what is the significance of the diagonal matrix, say $\Lambda$?
Why is Diagonalization important?Even more so, what about orthogonal Diagonalization? What do they signify?
Could you please elaborate.
[Sorry for asking so many questions at once, I am fairly new to Linear Algebra.]
Any help is Much Appreciated!