;
x = #(1, 2)~#(2, 3)
y = eigsm(x) ; spectral decomposition
y
;
det(x) - y.values[1] * y.values[2]
;
y.vectors'*y.vectors
;
z = y.vectors *diag(y.values) *y.vectors'
z
;
xinv = y.vectors*inv(diag(y.values))*y.vectors'
xinv
inv(x)
;
x = #(1, 2, 3)~#(2, 3, 4)
y = svd(x) ; singular value decomposition
y
;
xx = y.u *diag(y.l) *y.v'
xx
;
x = #(1, 2)~#(2, 3)
lu = ludecomp(x) ; LU decomposition
lu
;
index(lu.l*lu.u,lu.index)
;
library("xplore") ; unit is in library xplore!
x = #(2,2)~#(2,3)
tmp = chold(x, rows(x))
d = diag(xdiag(tmp)) ; diagonal matrix
b = tmp-d+unit(rows(tmp)) ; lower triangular
L = b'*sqrt(d) ; Cholesky triangular
;
x - L*L'