IssaRice: Created page with "==Notation== Axler writes $\mathcal M(T, (v_1,\ldots, v_n), (u_1, \ldots, u_m))$ . Axler never abbreviates bases, although if he did, the notation would look like <..."

2019-01-06T22:20:02Z

Created page with "==Notation== Axler writes <math>\mathcal M(T, (v_1,\ldots, v_n), (u_1, \ldots, u_m))</math>. Axler never abbreviates bases, although if he did, the notation would look like <..."

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==Notation==

Axler writes <math>\mathcal M(T, (v_1,\ldots, v_n), (u_1, \ldots, u_m))</math>. Axler never abbreviates bases, although if he did, the notation would look like <math>\mathcal M(T, \beta, \beta')</math> where <math>\beta := (v_1,\ldots, v_n)</math> and <math>\beta' := (u_1, \ldots, u_m)</math>.

Tao writes <math>[T]_\beta^{\beta'}</math>, where the "in" basis is a subscript and the "out" basis is a superscript. With vectors, <math>[v]_\beta</math> is a row vector and <math>[v]^\beta</math> is a column vector. This means that we can write <math>[T]_\beta^{\beta'} [v]^\beta = [v]^{\beta'}</math> and think of the lower <math>\beta</math> canceling out the upper <math>\beta</math>.

Treil writes <math>[T]_{\beta'\beta}</math> or sometimes <math>[T]_{\beta',\beta}</math>. With vectors, we can write <math>[T]_{\beta',\beta} [v]_\beta = [v]_{\beta'}</math> so that the bases "balance".

User:IssaRice/Linear algebra/Matrix of a linear transformation - Revision history

IssaRice: Created page with "==Notation== Axler writes \mathcal M(T, (v_1,\ldots, v_n), (u_1, \ldots, u_m)). Axler never abbreviates bases, although if he did, the notation would look like <..."

IssaRice: Created page with "==Notation== Axler writes $\mathcal M(T, (v_1,\ldots, v_n), (u_1, \ldots, u_m))$ . Axler never abbreviates bases, although if he did, the notation would look like <..."