How to do matrix exponential operation in Stata?

[Yao Zhao]

matrix A = (1,0,0,0,0\0.6,0,.4,0,0\0,.6,0,.4,0\0,0,.6,0,.4\0,0,0,0,1)
matrix list A
matrix B = A*A

I know how to do A^2. Now I want to do A^20. How should I do this?

Many thanks in advance!

[Sebastian Kripfganz]

1. You could do it in a loop:

matrix B = A
forvalues j = 2/20 {
    matrix B = B * A
}
matrix list B

2. Given that your matrix is diagonalizable with only real eigenvalues, you could use the eigenvalue decomposition, which is easier done in Mata:

mata:
    A = st_matrix("A")
    eigensystem(A, V, L)
    B = V * diag(L:^20) * luinv(V)
    st_matrix("B", Re(B))
end
matrix list B

In case of a symmetric matrix, an even easier way would be to use the Mata function matpowersym().

[Nick Cox]

Use Mata is the best advice, but for how this was done in 1999

search matpow, stb historical