MathLiveTranspose of a matrix
The transpose of a matrix is obtained by swapping its rows and columns, so the entry in row i and column k of the transpose equals the entry in row k and column i of the original matrix. It is used throughout linear algebra for symmetry checks, inner products and solving systems.
\left( \boldsymbol{A}^{\mathrm{T}} \right)_{ik} = \left( \boldsymbol{A} \right)_{ki}What the symbols mean
| the original matrix | |
| the transpose of the matrix A | |
| row index of the transpose (column index of A) | |
| column index of the transpose (row index of A) |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledmatrix transpose, transpose, transpose matrix formula, matrix transpose entries, A transpose ij equals A ji
- SourceWikidata Q223683
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