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I am currently taking a course in linear algebra and on a lot of questions have this notation and the more I read about linear algebra online the more I see this notation:

$$2(-1, 2)^T\cdot(4,1)^T=4$$

Why to the power of T? I get that it is the transpose and how the transpose works, but why?

linker
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2 Answers2

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Not everybody does it this way, but the idea is that

  • the vectors we prefer to deal with, and the vectors we've defined dot products for, are column vectors, like $\begin{bmatrix}-1 \\ 2\end{bmatrix}$ and $\begin{bmatrix}4 \\ 1\end{bmatrix}$.
  • the notation $(-1,2)$ and $(4,1)$ denotes row vectors $\begin{bmatrix}-1 & 2\end{bmatrix}$ and $\begin{bmatrix}4 & 1\end{bmatrix}$.

To get column vectors out of the row vectors, we take the transpose.

Misha Lavrov
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As you mentioned, "to the power of T" is actually the transpose. Often people write the transpose of a (column) vector instead of the vector since it takes up less vertical space. It is pure notational convenience and can be useful in inline equations.

johnny10
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