Question

The notation Ak meas the matrix A Multiplied with itself k times (a) For the n×n diagonal matrices D having enteries dii,tha D2 is also diagonal with enteries dii(b)For the n×n diagonal matrices D what do you think the enteries of Dk are?

Answer 1

Explanation:

Let A and B be a diagonal matrices.

C=AB is a diagonal matrix. With cii=(aii)(bii) entries.

Then, if D is a diagonal matrix we have:

D2 is a diagonal matrix with entries d2ii=(dii)(dii)=(dii)^2

D3 is a diagonal matrix with entries d3ii=(dii)(dii)(dii)=(dii)^3

....

Dk is a diagonal matrix with entries dkii=(dii)^k