diagonal matrix

2020-11-17 LinearAlgebra shark 1 min read

Definition: a diagonal matrix is the one which has value zero on all off-diagonal elements. They are in the form

(1) $\begin{align*}D = \begin{bmatrix} c_1 & \cdots & 0 \\ \cdots & & \cdots \\ 0 & \cdots & c_n\end{bmatrix}\end{align*}$

Benefits: they allow faster computations for determinants, powers, and inverse.

Determinant: $det(D) = \prod_{i=1}^n c_i$ .

Inverse: $D^{-1} = \begin{bmatrix} \frac{1}{c_1} & \cdots & 0 \\ \cdots & & \cdots \\ 0 & \cdots & \frac{1}{c_n}\end{bmatrix}$

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