# 28_3 - Inverting Matrix AX = I X = A-1 How hard is the...

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

1 Matrix inversion Inverting Matrix ± AX = I X = A -1 ± How hard is the matrix inversion problem? Theorem: Multiplication is as hard as inversion Proof: Let I(n) be the cost of inversion. Let M(n) be the cost of multiplication. Want to show I(n) = Θ (M(n)). ± M(n)=O(I(n)) ± I(n) = O(M(n)) Inverting Matrix ± AX = I X = A -1 ± How hard is the matrix inversion problem? Theorem: Multiplication is as hard as inversion Proof: Let I(n) be the cost of inversion. Let M(n) be the cost of multiplication. Want to show I(n) = Θ (M(n)). ± M(n)=O(I(n)) ± I(n) = O(M(n)) example ± Two other problems: ± Multiplication of two n-digit numbers x and y ± Squaring one n-digit number z ± Which problem is harder (assuming +/- can be done easily)? xy = ((x+y) 2 -(x-y) 2 )/4 Inverting Matrix ± M(n)=O(I(n)) Consider A, B, C s.t. AB = C Construct ± I(n) = O(M(n)) I DD I B I AB A I D I B I A I D n n n n n n = = = 1 1 0 0 0 0 0 0 0 , , . 3 assumming )), ( ( ) ( )

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 document was uploaded on 02/21/2011.

### Page1 / 2

28_3 - Inverting Matrix AX = I X = A-1 How hard is the...

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

View Full Document
Ask a homework question - tutors are online