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## Elem Linear Algebra

by: Henderson Lind II

9

0

2

# Elem Linear Algebra MATH 342

Henderson Lind II
UO
GPA 3.8

Dev Sinha

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COURSE
PROF.
Dev Sinha
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Henderson Lind II on Tuesday September 8, 2015. The Class Notes belongs to MATH 342 at University of Oregon taught by Dev Sinha in Fall. Since its upload, it has received 9 views. For similar materials see /class/187176/math-342-university-of-oregon in Mathematics (M) at University of Oregon.

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Date Created: 09/08/15
Summary of theorems from Math 342 De nition 1 Let B b1L7 7bn arid C C1 7on be two bases for a vector space V 1 The charige of basis matricc MCng is the matria with the property that if Mg 2 theri M B 1 Mceoivigic39 That is7 the coordinates of v with respect to the C basis are those with respect to the 8 basis multiplied by the matrix MCHB Proposition 2 The matrices MCng arid Mgnc are iriverse matrices Theorem 3 Let B b1L7 7bn arid C C1 7en be two bases for a vector space V Theri the charige of matria from B to C namely MCHB has as its ith column the vector bic the coordinates of the ith basis vector ofB with respect to the C basis De nition 4 IfB is a basis for V and T V a V is a linear transformation then the matricc which represents T with respect to the 8 basis Tg is the matrip with the property that for any vector v Tikg Tgvg More generally ifC is a basis for W and T V a W is a linear transformation then the matricc which represents T with respect to B andC satis es Tvc The 15 That is Tg is the matrix which encodes the effect of the linear transformation T Theorem 5 IfB is a basis for V and T V a V is a linear transformation then the matricc Tg has as its ith column the vector Tbg the B coordinates ofT applied to the ith basis vector of B More generally ifC is a basis for W and T V a W is a linear transformation then the ith column vector of T5 is TbC Theorem 6 Let B b1 bn and C C1 cn be two bases for a vector space V and T V a V a linear transformation Then TC MchngMghc

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