Expectation of a constant diagonal matrix

1. What matrix is one with constant diagonals?
2. What is the expectation of a matrix?
3. What is the eigenvalues of a diagonal matrix?
4. What if the diagonal elements of matrix are equal?

What matrix is one with constant diagonals?

A Hankel matrix. A square diagonal matrix, with all entries on the main diagonal equal to 1, and the rest 0.

What is the expectation of a matrix?

The expected value of a matrix is defined as the matrix of expected values. = [E(Xi,j) + E(Yi,j)] = [E(Xi,j)] + [E(Yi,j)] = E(X) + E(Y).

What is the eigenvalues of a diagonal matrix?

The eigenvalues of A are the zeros of the characteristic polynomial: p(λ)=(−1 − λ)(−1 − λ) − 2=(λ + 1)2 − 2. So the eigenvalues are λ = −1 ± √ 2.

What if the diagonal elements of matrix are equal?

If all entries on the main diagonal are equal scalars, then the diagonal matrix is called a scalar matrix.