Matrix Operations

Calculation Results & Process

💡 Quick Guide to Matrix Sum & Product

• Matrix Addition & Subtraction: Can only be performed on matrices of the exact same size (dimensions). Simply add or subtract the corresponding elements in the same positions.
• Matrix Multiplication (Product): The number of columns in Matrix A must equal the number of rows in Matrix B. The element $c_{ij}$ of the result matrix $C = A \cdot B$ is calculated as the dot product (sum of products) of the $i$-th row of Matrix A and the $j$-th column of Matrix B: $$c_{ij} = \sum_{k=1}^{n} a_{ik}b_{kj}$$ Therefore, matrix multiplication is generally non-commutative, i.e., $A \cdot B \neq B \cdot A$.