Matrix-Vector Multiplication
Calculates the product of a matrix and a vector. The result of the product is a vector.
| \(\hspace{30px}Ax=c\\ \normalsize{\left[\begin{array}\\ a_{\small 11}& \cdots& a_{\small 1j}\\ a_{\small 21}& \cdots& a_{\small 2j}\\ \vdots& \ddots& \vdots\\a_{\small i1}& \cdots& a_{\small ij}\\\end{array}\right]} \normalsize{\left(\begin{array}\\ x_1\\ x_2\\\vdots\\x_j\\\end{array}\right)} =\normalsize{\left(\begin{array}\\ \sum a_{1j}x_j\\ \sum a_{2j}x_j\\\vdots\\\sum a_{ij}x_j\\\end{array}\right)}\\ \) |
The matrix-vector product Ax is possible only when the number of columns in A is equal to the dimension of x.
| \(Ax=c\hspace{30px}\normalsize c_{i}={\large\displaystyle \sum_{\tiny j}}a_{ij}x_{j}\\\) |
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