Hi. Very short code. Singular Value Decomposition using QR decomposition.

svd.sm (59 KiB) downloaded 127 time(s).
svd.pdf (142 KiB) downloaded 139 time(s).

Best regards.
Alvaro.

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

svd_nr.pdf (122 KiB) downloaded 108 time(s).
svd_nr.sm (95 KiB) downloaded 94 time(s).

Best regards.
Alvaro.

Wrote

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

Thanks Alvaro ... OK all red SS 6179
I have no applications for the rectangular matrix.
Ultimately, all that stuff aims at solving singular square matrix,
2 examples Chemical Balance all done well.
Smath SVD can be used as well to sanity Greville.
Both documents take no time calculation.

Maths Pseudo Greville.sm (87 KiB) downloaded 98 time(s).
Maths SVD.sm (228 KiB) downloaded 101 time(s).

Wrote

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

Complete sanity vs Smath built-in SVD ... hyper fast.
Thanks Alvaro for sharing your great programming skill.

Maths svd.nr.sm (94 KiB) downloaded 100 time(s).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91 KiB) downloaded 74 time(s).
pinv.pdf (168 KiB) downloaded 78 time(s).

Best regards.
Alvaro.

Pseudo inverse, based in the previous (improved) SVD.

pinv_svd.sm (161 KiB) downloaded 102 time(s).
pinv_svd.pdf (153 KiB) downloaded 99 time(s).

Best regards.
Alvaro.