MathLiveTrace of a matrix
The trace of a square matrix is the sum of the entries on its main diagonal. It is used in linear algebra for matrix invariants, similarity checks, and as the sum of eigenvalues.
\operatorname{tr}(\mathbf{A}) = \sum_{i} A_{ii}What the symbols mean
| a square matrix | |
| the diagonal entry in row and column i | |
| index running over the rows (and columns) of the matrix |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledtrace of square matrix, sum of diagonal elements, matrix trace formula, tr A, trace of matrix
- SourceWikidata Q321102
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “trace of a matrix”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.