I have a matrix $S$:
tensor([[ 0.3600, 0.2100, 0.4300, -0.0000],
[ 0.2100, 0.9300, -0.1400, 0.0000],
[ 0.4300, -0.1400, 0.7100, -0.0000],
[ 0.0000, -0.0000, -0.0000, 1.0000]])
and matrix $M$:
tensor([[0.3658, 0.3338, 0.1566, 0.1438],
[0.2850, 0.3646, 0.1580, 0.1924],
[0.3979, 0.2923, 0.1555, 0.1544],
[0.3177, 0.3192, 0.2076, 0.1556]])
It turns out product $SM$ is very close to $M$, even though $S$ is far from identity matrix. What is the name of this property of matrices $S$ with respect to $M$?
To be clear, matrix $S$ was produced by multiplying matrix $Q$ by it's pseudoinverse $Q^+$
Q
tensor([[0.3333, 0.3333, 0.3333],
[0.0000, 1.0000, 0.0000],
[0.5000, 0.0000, 0.5000],
[0.0000, 0.0000, 1.0000]])
Q+
tensor([[ 0.8570, -0.2860, 1.4290, -1.0000],
[ 0.2140, 0.9290, -0.1430, 0.0000],
[ 0.0000, -0.0000, -0.0000, 1.0000]])