diagonal matrix is invertible if and only if the entries are all nonzero. In this case, we have

In particular, the diagonal matrices form a subring of the ring of all -by- matrices.

Multiplying an -by- matrix from the left with amounts to multiplying the -th row of by for all ; multiplying the matrix from the right with amounts to multiplying the -th column of by for all .

Operator matrix in eigenbasis

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