Linear Algebra - Column Vector (One-column matrix)

A vector can be (seen|interpreted) as a one-column matrix. To get a one-row matrix, use Linear Algebra - Matrix.

Multiplication with a matrix

Multiplying a matrix A by a one-column matrix B:

$$A * b = \begin{bmatrix}\begin{array}{rrr} & & \\ & \large{A} & \\ & & & \end{array}\end{bmatrix} * \begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}$$

By matrix-vector definition of matrix-matrix multiplication, result is:

• a matrix with one column: A * b
• that you can interpret as a vector (a “column vector”)

Convention

• Write vector $[1, 2, 3]$ as $\begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}$
• Write $A * [1, 2, 3]$ as $\begin{bmatrix}\begin{array}{ccc} & & \\ & \large{A} & \\ & & & \end{array}\end{bmatrix} * \begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}$ or A*b

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