# linear algebra – Maximal rank resolution to \$W^+Y = W^+WX\$ Answer

Hello pricey customer to our community We will proffer you an answer to this query linear algebra – Maximal rank resolution to \$W^+Y = W^+WX\$ ,and the respond will breathe typical by means of documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning in regards to the respond to this query.

linear algebra – Maximal rank resolution to \$W^+Y = W^+WX\$

Let $$X in mathbb{R}^{a occasions n}$$ and $$Y in mathbb{R}^{b occasions n}$$. How can we discover a matrix $$W in mathbb{R}^{b occasions a}$$ of maximal rank, such that
$$W^+Y = W^+WX$$
(or alternatively, $$WW^+Y = WX$$) the place $$W^+$$ denotes the pseudoinverse of $$W$$? We concern in regards to the $$W$$ of maximal rank, as one may trivially take $$W$$ to breathe all zeros and the equation would maintain. From a geometrical perspective, we’re searching for a $$W$$ such that when $$X$$ is mapped to the column house of $$W$$, and $$Y$$ is mapped to the row house of $$W$$, these two photos are equal when one considers the canonical isomorphism between the row and column house of $$W$$. In illustration it is needful, we are able to occupy that $$X$$ and $$Y$$ have complete rank.

we are going to proffer you the answer to linear algebra – Maximal rank resolution to \$W^+Y = W^+WX\$ query by way of our community which brings all of the solutions from a number of dependable sources.