What is Diagonal matrix: Definition and 55 Discussions

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 2×2 diagonal matrix is




[





3


0




0


2





]



{\displaystyle \left[{\begin{smallmatrix}3&0\\0&2\end{smallmatrix}}\right]}
, while an example of a 3×3 diagonal matrix is




[





6


0


0




0


7


0




0


0


4





]



{\displaystyle \left[{\begin{smallmatrix}6&0&0\\0&7&0\\0&0&4\end{smallmatrix}}\right]}
. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix.
A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size). Its determinant is the product of its diagonal values.

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