User:IssaRice/Linear algebra/Matrix of a linear transformation
Axler writes . Axler never abbreviates bases, although if he did, the notation would look like where and .
Tao writes , where the "in" basis is a subscript and the "out" basis is a superscript. With vectors, is a row vector and is a column vector. This means that we can write and think of the lower canceling out the upper .
Treil writes or sometimes . With vectors, we can write so that the bases "balance".