```⍝ Cholesky decomposition of Hermitian positive-definite matrix:

x←t+.×⍉t←¯10+?5 5⍴20
x
111  106   22  ¯85  ¯14
106  198  ¯91 ¯150   69
22  ¯91  196   22 ¯118
¯85 ¯150   22  166  ¯77
¯14   69 ¯118  ¯77  151

y←Cholesky x
y
10.53565375    0            0            0           0
10.06107475    9.837417078  0            0           0
2.088147591 ¯11.38601811   7.873895557  0           0
¯8.067842964  ¯6.996636239 ¯5.183835597  5.008476789 0
¯1.328821194   8.373068735 ¯2.525981305 ¯8.432039953 1.282994497

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).

DCT ⎕DCT ← ⎕DCT ⎕CT

z←t+.×+⍉t←(¯10+?5 5⍴20)+0j1×¯10+?5 5⍴20
z
268     ¯171      ¯78J085 ¯104J¯031  43J0054
¯171      457     ¯190J¯30  120J¯106  40J¯162
¯78J¯85 ¯190J030  285       33J0004 ¯34J0045
¯104J031  120J106   33J¯04  467      107J0116
43J¯54   40J162  ¯34J¯45  107J¯116 228

y←Cholesky z

z ≡ y +.× +⍉y
1

⎕DCT ← DCT

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