start T in matrix equation

In many start equations I see T (transpose) or -1 (inverse). Why is there using T, but not original matrix?

Example https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula ($$\mathbf{A}$$ + $$\mathbf{U}$$*$$\mathbf{Q}^\top$$)

Why is there transpose matrix in start is more practical then use in other part? In start conditions we have $$\mathbf{Q}$$, but not $$\mathbf{Q}^\top$$.

With kind regards.

1 Answer

In Morrison’s formula the $$u$$ and $$v$$ are column vectors. It is more natural to say both are (column) vectors and write $$uv^T$$ than to say that $$u$$ is a column vector and $$v$$ a row vector.