Scalar transformation

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. The term usually refers to square matrices. An example of a 2-by-2 diagonal matrix is ${\displaystyle {\begin{bmatrix}3&0\\0&2\end{bmatrix}}}$; the following matrix is a 3-by-3 diagonal matrix:${\displaystyle {\begin{bmatrix}6&0&0\\0&7&0\\0&0&19\end{bmatrix}}}$. An identity matrix of any size, or any multiple of it, will be a diagonal matrix.

As stated above, the off-diagonal entries are zero. That is, the matrix D = (d_i,j) with n columns and n rows is diagonal if

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