proof of block determinants

If A-1 exists, then




Each of the first matrices in the decompositions are triangular. Hence their determinantsMathworldPlanetmath equal 1. This means that the determinant of the original matrix equals the determinant of either of the second matrices in the decomposition. Therefore


The second formula follows by using a similar trick.

Title proof of block determinants
Canonical name ProofOfBlockDeterminants
Date of creation 2013-03-22 15:27:49
Last modified on 2013-03-22 15:27:49
Owner georgiosl (7242)
Last modified by georgiosl (7242)
Numerical id 5
Author georgiosl (7242)
Entry type Proof
Classification msc 15A15