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# lecture15 - Lecture 15 Recursive and Iterative Formula for...

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Lecture 15 Recursive and Iterative Formula for Determinants Shang-Hua Teng

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Pseudo-Hypercube or Pseudo-Box n-Pseudo-Hypercube For any n affinely independent vectors ( 29 { } + + + + = n i c p c p c p c c p p p n n n 1 , 1 , 0 : 0 convex , , , cube i 2 2 1 1 0 2 1 n p p p , , , 2 1
Determinant of Square Matrix [ ] [ ] ( 29 ( 29 , , , cube volume , , , , , , det 2 1 2 1 2 1 n n n p p p p p p p p p = = How to compute determinant or the volume of pseudo-cube?

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Properties of Determinant 1. det I = 1 2. The determinant changes sign when sign when two rows are changed (sign reversal) 1. Determinant of permutation matrices are 1 or -1 1. The determinant is a linear function of each row separately 1. det [ a 1 , …,t a i ,…, a n ] = t det [ a 1 , …, a i ,…, a n ] 2. det [ a 1 , …, a i + b i ,…, a n ] = det [ a 1 , …, a i ,…, a n ] + det [ a 1 , …, b i ,…, a n ]
Properties of Determinant and Algorithm for Computing it [4] If two rows of A are equal, then det A = 0

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## This note was uploaded on 03/08/2010 for the course CS 232 taught by Professor Bera during the Spring '09 term at BU.

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lecture15 - Lecture 15 Recursive and Iterative Formula for...

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