[ 机器学习 - 吴恩达 ] Linear Algebra review | 3-2 Addition and scalar (标量) multiplication

Matrix Addition

\[\begin{bmatrix} 1&0\\ 2&5\\ 3&1\\ \end{bmatrix}+\begin{bmatrix} 4&0.5\\ 2&5\\ 0&1\\ \end{bmatrix}=\begin{bmatrix} 5&0.5\\ 4&10\\ 3&2\\ \end{bmatrix}\]

Note: 矩阵维度必须相同

Scalar Multiplication

Scalar=real number: 标量

\[3\times\begin{bmatrix} 1&0\\ 2&5\\ 3&1\\ \end{bmatrix}=\begin{bmatrix} 3&0\\ 6&15\\ 9&6\\ \end{bmatrix}=\begin{bmatrix} 1&0\\ 2&5\\ 3&1\\ \end{bmatrix}\times3\]

\[\begin{bmatrix} 4&0\\ 6&3\\ \end{bmatrix}/4=\frac14\begin{bmatrix} 4&0\\ 6&3\\ \end{bmatrix}=\begin{bmatrix} 1&0\\ \frac32&\frac34\\ \end{bmatrix}\]

Combination of Operands

\[3\times\begin{bmatrix} 1\\ 4\\ 2\\ \end{bmatrix}+\begin{bmatrix} 0\\ 0\\ 5\\ \end{bmatrix}-\begin{bmatrix} 3\\ 0\\ 2\\ \end{bmatrix}/3=\begin{bmatrix} 2\\ 12\\ 10\frac13\\ \end{bmatrix}\]

3 x 1 matrix or 3-dimensional vector