#N canvas 366 49 705 646 10; #X text 347 472 updated for; #X obj 435 472 iemmatrix 0.2; #X obj 484 498 matrix; #X text 354 497 see also help for; #X text 243 142 singular; #X text 245 107 regular; #X text 246 158 regular; #X text 247 168 but badly conditioned; #X text 154 533 A*inv(A)=inv(A)*A=I; #X text 248 221 pseudoinverse: P1=inv(A'*A)*A'; #X text 247 269 pseudoinverse: P2=A'*inv(A*A'); #X text 245 553 P1*A=I; #X text 245 573 A*P2=I; #X obj 92 199 mtx 3; #X msg 112 164 1 2 3 2 4 4 3 4 5; #X msg 92 108 1 2 4 2 3 4 3 4 5; #X obj 92 472 mtx_print inverse; #X obj 92 300 t a a; #X obj 134 300 mtx_print original; #X obj 153 219 mtx_rand 4 3; #X msg 153 198 bang; #X msg 153 248 bang; #X obj 153 269 mtx_rand 3 4; #X obj 182 348 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1 -1; #X text 199 359 instability detected!; #X obj 92 348 mtx_pinverse; #X text 45 16 mtx_pinverse:: get the inverse of a matrix (with pivoting) ; #X text 44 49 mtx_pinverse calculates the inverse of a square-matrix. For inverting rectangle matrices \, use [mtx_inverse] or [mtx_pseudoinverse] ; #X msg 103 140 1 2 3 2 3 4 0 0 0; #X text 194 385 due to pivoting \, [mtx_pinverse] will handle badly conditioned matrices better than [mtx_inverse] \, however it will also detect less (real) instabilities than [mtx_inverse]; #X obj 485 524 mtx_inverse; #X obj 485 548 mtx_pseudoinverse; #X connect 13 0 17 0; #X connect 14 0 13 0; #X connect 15 0 13 0; #X connect 17 0 25 0; #X connect 17 1 18 0; #X connect 19 0 17 0; #X connect 20 0 19 0; #X connect 21 0 22 0; #X connect 22 0 17 0; #X connect 25 0 16 0; #X connect 25 1 23 0; #X connect 28 0 13 0;