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Let $A$ be a $m \times n$ matrix,
$$A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ 
a_{21} & a_{22} & \cdots & a_{2n} \\ 
\vdots & \vdots & \cdots & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn} \\ 
\end{bmatrix}$$

We can also write it as
$$A = \begin{bmatrix} c_{1} & c_{2} & \cdots & c_{n}\end{bmatrix}$$

where $c_i$ represents a column vector 
$$c_i = \begin{bmatrix} a_{1i} \\
a_{2i} \\
\vdots \\
a_{mi}
\end{bmatrix}$$

You can either see a row matrix as a transpose of a column matrix or as a points of real line. I mean, see as you know that
$$B = \begin{bmatrix} 1 & 2 \\
-3 & 0
\end{bmatrix}$$

represents two vectors in the plane $\begin{bmatrix} 1 \\ -3
\end{bmatrix}$ and $\begin{bmatrix} 2 \\ 0\end{bmatrix}$.

In the same way we can see that row matrix just represents a points, I guess.
$$M = \begin{bmatrix} 1 & 5 & 9
\end{bmatrix}$$
may just represents points in real line as it is $1 \times 3$ so,

But it has definitely nothing to do with squeezing or shifting. Those are totally different concepts.

Fri, 10 May 2024 05:06 GMT