Editing Diagonal matrix (section)

== Properties ==

* The [[determinant]] of {{math|diag(''a''<sub>1</sub>, ..., ''a''<sub>''n''</sub>)}} is the product {{math|''a''<sub>1</sub>⋯''a''<sub>''n''</sub>}}.
* The [[adjugate]] of a diagonal matrix is again diagonal.
* Where all matrices are square,
** A matrix is diagonal if and only if it is triangular and [[normal matrix|normal]].
** A matrix is diagonal if and only if it is both [[triangular matrix|upper-]] and [[triangular matrix|lower-triangular]].
** A diagonal matrix is [[symmetric matrix|symmetric]].
* The [[identity matrix]] {{math|'''I'''<sub>''n''</sub>}} and [[zero matrix]] are diagonal.
* A 1×1 matrix is always diagonal.
* The square of a 2×2 matrix with zero [[trace (linear algebra)|trace]] is always diagonal.