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

svd.sm (59.92 KiB) downloaded 800 time(s).
svd.pdf (142.85 KiB) downloaded 454 time(s).

Best regards.
Alvaro.

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

svd_nr.pdf (122.43 KiB) downloaded 419 time(s).
svd_nr.sm (95.26 KiB) downloaded 770 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 793 time(s).
Maths SVD.sm (228.82 KiB) downloaded 785 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 830 time(s).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91.35 KiB) downloaded 748 time(s).
pinv.pdf (168.98 KiB) downloaded 390 time(s).

Best regards.
Alvaro.

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

pinv_svd.sm (161.03 KiB) downloaded 761 time(s).
pinv_svd.pdf (153.64 KiB) downloaded 420 time(s).

Best regards.
Alvaro.