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Suppose I have a matrix $C=\begin{bmatrix} 1 & 0 \end{bmatrix}$ and a vector $\mathbf{x}=\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$.

I want to write the matrix product $C\mathbf{x}$, should the answer be vector notation (bold) or not?

I mean vector notation $$\mathbf{y}= C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=x_1 $$ or scalar notation $$ y= C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=x_1 $$ I use upright letters for matrices, bold letters for vectors. Non-bold for scalars.

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$$C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=[x_1]$$ (note the brackets around $x_{1}$) is a

  • $1 \times 1$ matrix, or
  • a row vector of length one, or
  • a column vector of length one,

you choose.

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  • $\begingroup$ Thanks! But using scalar notation $y$ (not bold) is wrong? $\endgroup$ – JDoeDoe Dec 21 '16 at 11:48
  • $\begingroup$ The only reason to choose a particular notation is to please your instructor ;-) $\endgroup$ – Andreas Caranti Dec 21 '16 at 11:52

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