I am trying to (pseudo)solve a linear system $Ax=y$. I have a matrix A
, and 2 vectors x
and y
A = {
{1, 1, 1, 0},
{1, 1, 0, 1},
{0, 1, 1, 0},
{0, 1, 0, 1}};
x = {pcv, pcf, pat, pnt};
y = {p11, p00, p10, p01};
Reading Wikipedia, I expect to obtain A.PseudoInverse[A].y == y
. However I obtain
In[4]:= A.PseudoInverse[A].y
Out[4]= {p00/4 - p01/4 + p10/4 + (3 p11)/4, (3 p00)/4 + p01/4 - p10/4 + p11/4,
-(p00/4) + p01/4 + (3 p10)/4 + p11/4, p00/4 + (3 p01)/4 + p10/4 - p11/4}
What am I missing?
I expect to obtain A.PseudoInverse[A].y == y
this will be true ifA
is not singular which is not in your case. $\endgroup$Det[A] == 0
. $\endgroup$A.pA.A== A (Wikipedia, pA=PseudoInverse[A]) => A.pA.y==y
is dangerous. $\endgroup$