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

svd.sm (59.92 KiB) downloaded 748 time(s).
svd.pdf (142.85 KiB) downloaded 431 time(s).

Best regards.
Alvaro.

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

svd_nr.pdf (122.43 KiB) downloaded 398 time(s).
svd_nr.sm (95.26 KiB) downloaded 721 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 (87.79 KiB) downloaded 747 time(s).
Maths SVD.sm (228.82 KiB) downloaded 737 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 (94.98 KiB) downloaded 774 time(s).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91.35 KiB) downloaded 704 time(s).
pinv.pdf (168.98 KiB) downloaded 364 time(s).

Best regards.
Alvaro.

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

pinv_svd.sm (161.03 KiB) downloaded 712 time(s).
pinv_svd.pdf (153.64 KiB) downloaded 397 time(s).

Best regards.
Alvaro.