$ax$ means apply transformation $a$ on $x$, we can look at the null space and range of a and have an understanding of what's going to happen to the vector after we apply transformation $a$. just ... linear-algebra linear-transformations quadratic-forms asked feb at : akhilv bronze badge votes answer...
and satisfy $u*t=\mathrm{id}_v$ or $tu=\mathrm{id}_w$, then t is an isomorphism. (... linear-algebra reference-request linear-transformations asked yesterday twilight bronze badges vote answers views let v,w and z be finite-dimensional subspaces and let $t: v ightarrow w$, $s: w ightarrow z$ be linear...
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