Thread: upper triangular matrix

An mxn matrix is one whose entries below the main diagonal's are zeros. When is a square upper triangular matrix invertible?

Originally Posted by cottekr

An mxn matrix is one whose entries below the main diagonal's are zeros. When is a square upper triangular matrix invertible?

ANY square matrix is invertible iff its determinant is not zero. The question thus is: what's the determinant of a triangular (upper or lower, it's the same) matrix? Think of it, the answer is surprisingly simple.

Tonio