```y ← ##.Cholesky x       ⍝ decomposition of Hermitian positive-definite matrix.

From Roger Hui: see http://www.jsoftware.com/jwiki/Essays/Cholesky%20Decomposition
for the derivation.

Examples:

x←t+.×⍉t←¯10+?5 5⍴20
x
153  ¯14   10 ¯117 ¯48
¯14  286 ¯158 ¯203  72
10 ¯158  178  112  ¯3
¯117 ¯203  112  274 ¯16
¯48   72   ¯3  ¯16  49

y←Cholesky x
y
12.3693     0       0         0        0
¯1.13183   16.8736  0         0        0
0.808452  ¯9.3095  9.52258   0        0
¯9.45889  ¯12.6651  0.182868  4.90831  0
¯3.88057    4.00672 3.93148  ¯0.545884 1.46044
x ≡ y +.× ⍉y
1

⍝ The t+.×⍉t construct is a handy way to generate a Hermitian, positive definite
⍝ matrix. For real numbers, "Hermitian" is the same as symmetric (x≡⍉x); for
⍝ complex matrices; Hermitian means z≡+⍉z (conjugate transpose).

z←t+.×+⍉t←(¯10+?5 5⍴20)+0j1×¯10+?5 5⍴20
z
310       ¯51J¯092   93J0157 ¯31J145  244J¯024
¯51J0092  357      ¯149J¯054  54J060 ¯192J0203
93J¯157 ¯149J0054  217      ¯16J115  113J¯203
¯31J¯145   54J¯060  ¯16J¯115 397       10J¯048
244J0024 ¯192J¯203  113J0203  10J048  384

y←Cholesky z

z ≡ y +.× +⍉y
1

⍝ So the Cholesky decomposition is a sort of "square root" y of a Hermitian
⍝ positive matrix z, such that y is lower-triangular and z≡y+.×+⍉y.