Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online lexicon: Annotation to

Determinants of Special Matrices


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

For some special types of $ n\times n$-matrices $ A$ the determinant can be given immediately.

(i)
Triangular matrices: If $ a_{i,j}=0$ for $ i<j$ or $ i>j$, then we can calculate the determinant by

$\displaystyle \operatorname{det}A = a_{1,1}\cdots a_{n,n}\,
.
$

(ii)
Block-diagonal matrices: If matrix $ B$ has a blocked structure with $ A_{i,j}=0$, $ i\neq j$ and square diagonal blocks, then we have

$\displaystyle \operatorname{det}B = \prod\limits_{i=1}^k \operatorname{det}A_{i,i}\,.
$

(iii)
For a unitary matrix $ U$ we have

$\displaystyle \vert\operatorname{det}U\vert=1\,.
$

In particular, for orthogonal matrices $ (u_{i,j}\in \mathbb{R})$ we have

$\displaystyle \operatorname{det}U \in \{-1,1\}\,.
$


(temporary unavailable)

[Back]

  automatisch erstellt am 19.  8. 2013