Consider the square of A using eigen() function in R.
We know that, for A = V x D x V^(-1) then A^n = V x D^n x V^(-1), where columns of V contains the eigenvectors of A and D is a diagonal matrix with eigenvalues of A on the diagonal.
` [,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
A = [3,] 3 7 11 15
[4,] 4 8 12 16 `
The result should be same as A*A
` [,1] [,2] [,3] [,4]
[1,] 90 202 314 426
[2,] 100 228 356 484
[3,] 110 254 398 542
[4,] 120 280 440 600 `
I have tried
V <- eigen(A)$vectors
square_dia <- diag(eigen(A)$values,4,4)
D <- diag(A)*diag(A)
But I couldn't get the result I desired.
I do get these results matching. Perhaps you confused %*% (matrix product) with * (elementwise/Hadamard product) somewhere?
V <- eigen(A)$vectors
D <- diag(eigen(A)$values)
M1 <- V %*% D^2 %*% solve(V)
M2 <- A %*% A
all.equal(M1, M2) ## TRUE
You may be interested in the %^% (matrix power) operator from the expm package ...