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

svd.sm (59 KiB) downloaded 112 time(s).
svd.pdf (142 KiB) downloaded 122 time(s).

Best regards.
Alvaro.

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

svd_nr.pdf (122 KiB) downloaded 93 time(s).
svd_nr.sm (95 KiB) downloaded 79 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 83 time(s).
Maths SVD.sm (228 KiB) downloaded 87 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 85 time(s).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91 KiB) downloaded 60 time(s).
pinv.pdf (168 KiB) downloaded 62 time(s).

Best regards.
Alvaro.

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

pinv_svd.sm (161 KiB) downloaded 87 time(s).
pinv_svd.pdf (153 KiB) downloaded 81 time(s).

Best regards.
Alvaro.