MathLiveMatrix multiplication
Gives each entry of the product of two matrices as the sum of products of entries from a row of the first matrix and a column of the second. It is used whenever two compatible matrices are multiplied in linear algebra.
\left(\mathbf{A}\mathbf{B}\right)_{ik} = \sum_{j} A_{ij} B_{jk}What the symbols mean
| first matrix, of size i by j | |
| second matrix, of size j by k | |
| entry in row i and column k of the product matrix | |
| entry in row i and column j of matrix A | |
| entry in row j and column k of matrix B | |
| summation index running over the shared inner dimension |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledmatrix product, product of matrices, multiply two matrices, matrix product formula, row times column multiplication
- SourceWikidata Q1049914
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