Main diagonal

From Free net encyclopedia

In linear algebra, the main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal:

<math>\begin{bmatrix}

1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}</math>

A square matrix like the above in which the entries outside the main diagonal are all zero is called a diagonal matrix. The sum of the entries on the main diagonal of a matrix is known as the trace of that matrix.ca:Diagonal principal de:Diagonale (Lineare Algebra) es:Diagonal principal fr:Diagonale principale it:Diagonale principale he:אלכסון ראשי nl:Hoofddiagonaal pl:Przekątna główna macierzy