So lately I'm very into linear algebra, but our teacher wrote something that doesn't really make sense on the boards. So in my understandings $T_{BB'}$ means the matrix of change from $B$ to $B'$, simply because this seems to be the most rational way of thinking, "FROM $B$ to $B'$". I'm just wondering what you guys think. So can someone who really knows this stuff help me with these indexes? $$ [v]_B = T_{BA} \ *\ [v]_A$$ $$ [f]_B = T_{BA}\ * \ [f]_A \ * \ T_{AB}$$ $$ [f(v)]_B = [f]_{AB} \ *\ [v]_A$$ Where $v$ is a vector, $T$ is the matrix of change of basis, $B$ and $A$ are basis and $f$ is a linear map (is it?).
Indexes messed up my mind
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linear-algebra
linear-transformations
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0$[u]_M$ is the vector $(u_1,\ldots, u_n)^T$, where $u = \sum_{i=1}^n u_i m_i$ (and $M = \{m_1,\ldots,m_n\}$). Otherwise stated, it's the representation of $u$ in the basis $M$. For $f$, $[f]_M= (a_{ij})$ is the matrix of $f$ in the basis $M$, i.e. $a_{ij}$ are such that $f(m_j) = \sum_{i=1}^n a_{ij} m_i$. And if $M,M'$ are two bases, $[f]_{MM'}=(b_{ij})$ such that $f(m_j ') = \sum_{i=1}^n b_{ij} m_i$. – 2017-01-19