Another approach:
NB. Subtract projection of x onto y from x, leaving x orthogonal to y
orthox =: [ - ] +/ . * %.
NB. Convert list to a column vector
entable =: ,:^:(1=#@$)
NB. For each column, take orthogonal part & append to previous columns
orthogonalize =: (] ,~ orthox&.|:)&entable/&.|:
]o =. orthogonalize 4 4 ?@$ 100
0.376604 _1.95486 _16.0435 48
_1.27576 _20.7855 54.7391 12
_0.461323 57.2098 18.8696 6
1.38657 0.440836 61 0
+/ . *"1/~ |:o NB. check orthogonality
3.90478 5.34905e_13 _5.54223e_13 _2.55795e_13
5.34905e_13 3709.01 _1.42109e_13 _9.66338e_13
_5.54223e_13 _1.42109e_13 7330.83 _2.70006e_13
_2.55795e_13 _9.66338e_13 _2.70006e_13 2484
Time me no timings! If I wanted speed I'd use LAPACK.
Henry Rich
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