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Apologies for a simple question but my textbook is horrible. I don't seem to understand what this notation means.

$$ \left[ \begin{array}{c} T \end{array} \right]_b^a $$

I was looking online for resources to help me understand and found the following question:

Suppose a basis for V = R3 is the set C = {(1, 0, 0), (1, 1, 0), (1, 1, 1)}. And the coordinate vector of an element (x, y, z) is $$ \left[ \begin{array}{c} x-y\\ y-z\\ z \end{array} \right] $$

How would you get the matrix representation of T. The solution is

$$ \left[ \begin{array}{c} 3&4&4\\ 1&1&2\\ 1&1&0 \end{array} \right] $$

but I don't seem to understand how to get there so can someone provide a brief explanation of what is going on?

Mayi
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  • What is the context in which you saw $[T]^a_b$? –  Nov 01 '16 at 00:50
  • Its is basically in the chapter of linear transformations and finite-dimensional vector spaces. The exact definition in the textbook is that this is called the linear transformation T with respect to he bases b for V and a for W where b = {v1, ..., vn} and a = {w1,...,wn} – Mayi Nov 01 '16 at 00:54
  • I also got the question from the following resource. https://math.dartmouth.edu/archive/m24w07/public_html/Lecture12.pdf – Mayi Nov 01 '16 at 00:55
  • ohh. okay thanks. i will check it out – Mayi Nov 01 '16 at 00:57
  • You might also read the answers to these questions: 1, 2. Note that others use different notations for this. For instance I write $[T]_{a\leftarrow b}$ because though I've seen the notation $[T]^a_b$ before, I feel my notation is more intuitive. –  Nov 01 '16 at 01:02

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