This means that the two matrices are simultaneously diagonalizable; they share a common eigenbasis. The general case is a bit more involved in that the restrictions to the invariant …

I'm trying to prove that de normalizer $N (T)$ of the subgroup $T\subset GL_n$ of diagonal matrices is the subgroup $P\in GL_n$ of generalized permutation matrices.

Mar 15, 2016 · When the diagonal matrix is on the right, it scales the columns of the matrix it is multiplying. when the diagonal matrix is on the left, it scales the rows. Since column-scaling …

Apr 8, 2019 · And the diagonal matrix is a matrix in which the entries outside the main diagonal are all zero, which means it is can't be equal to zero matrices. And I wonder the definition of …

The proof is OK but it would be good to prove first that the product of two diagonal matrices is the diagonla matrix obtained by multiplying the elements of the diagonal.

Sep 25, 2015 · Morover, the space of diagonal $2\times 2$ matrices is a subspace of the space of all $2\times 2$ matrices that is isomorphic to $\mathbb R^2$. Again, an explicit isomorphism is …

Jan 1, 2021 · Leaves to show the maximality. Indeed, one can show (seemingly) more, namely, that in each case, the diagonal matrices inside the given algebra are their own centraliser. To …

Apr 21, 2016 · 5 Yes. Assuming that your matrix is in fact diagonalizable (which will happen if all of the eigenvalues are distinct, but can also sometimes happen when you have repeated …

Feb 17, 2016 · Is there standard notation for the set of diagonal matrices? Specifically if the elements must be nonnegative, i.e. the matrix is positive semi-definite?

Dec 3, 2018 · Explore related questions matrices numerical-linear-algebra matrix-decomposition See similar questions with these tags.