I'm studying linear control theory (by "Control theory for linear systems" by Trentelman et al.) and there appears subspaces $$ \langle A \vert im \, B\rangle = im \,B + A \,im\, B + \ \ldots \ + A^{n-1}\,im\,B $$ and $$ \langle ker \, C\vert A\rangle= ker \, C \cap ker \, CA \cap \ \ldots \cap CA^{n-1}. $$
Unfortunately, I'm unable to find how to pronounce the left part of this formulas. Could anyone help me with this?
"<A|imB>": This represents the subspace formed by taking the images of $B$ under the powers of $A$. In simpler terms, it refers to the space spanned by the results obtained by applying $A$ to $B$ multiple times.
"<kerC|A>": This denotes the intersection of the kernel of $C$ with the powers of $A$. In simpler words, it represents the common elements shared between the null space of $C$ and the results obtained by applying $A$ multiple times.