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Lecture 23

# MATH 235 Lecture 23: Inner Product, Length, and Orthogonality

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School
University of Massachusetts Amherst
Department
Mathematics
Course
MATH 235
Professor
Yaping Yang
Semester
Spring

Description
4/25/2017 Sect 5.1 Inner Product, Length Orthogonal nher Product in Rn dot product nX1 un V theorem for CER E Rn (cemmulative) (distributive) u W 20, any Inner Product Length Len (norm) magnitude) def.: a Vector V is caled a unt us 1. find a und vector u in the same direction as V ex let Spa Subsbace. find a unit vectsr that is a basis of W 4/25/2017 Sect 5.1 Inner Product, Length Orthogonal nher Product in Rn dot product nX1 un V theorem for CER E Rn (cemmulative) (distributive) u W 20, any Inner Product Length Len (norm) magnitude) def.: a Vector V is caled a unt us 1. find a und vector u in the same direction as V ex let Spa Subsbace. find a unit vectsr that is a basis of WSO could also usc d V did an CCA us- vs) ER sa u, V U and V ate orth (porpondicular Theorem U and V an orthogonal ER et Z et W subspace is W (2 W) if def Z l Sr every VE W ortho der Com blemen na RN fact: W is over (0, 0, 0) R3, let W span i mal vector the p fact dim w t din W Comes firm dim (Al) rank (A) n RT, let W WI plane t
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