differential geometry w notes from teacher_Part_31

# differential geometry w notes from teacher_Part_31 - 61 3.1...

This preview shows pages 1–2. Sign up to view the full content.

3.1. EXTERIOR ALGEBRA 61 It is easy to see that there holds also δ i 1 ... i n - p l 1 ... l n - p ε j 1 ... j p l 1 ... l n - p = ( n - p )! ε j 1 ... j p i 1 ... i n - p The set of all n × n real matrices is denoted by Mat( n , R ). The determinant is a map det : Mat( n , R ) R that assigns to each matrix A = ( A i j ) a real number det A deﬁned by det A = X ϕ S n sign ( ϕ ) A 1 ϕ (1) ··· A n ϕ ( n ) , The most important properties of the determinant are listed below: Theorem 3.1.4 1. The determinant of the product of matrices is equal to the product of the determinants: det( AB ) = det A det B . 2. The determinants of a matrix A and of its transpose A T are equal: det A = det A T . 3. The determinant of the inverse A - 1 of an invertible matrix A is equal to the inverse of the determinant of A: det A - 1 = (det A ) - 1 4. A matrix is invertible if and only if its determinant is non-zero. The determinant of a matrix

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/26/2011 for the course MAT 4821 taught by Professor Wong during the Spring '10 term at FSU.

### Page1 / 2

differential geometry w notes from teacher_Part_31 - 61 3.1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online