EGR  6013  Part  2:    Linear  Algebra  

Lecture  11  10/18/2015  

Teaser  Problem  one  extra  point  can  be  added  to  quiz  category  (1  point)  

1 x 1 = 1 11 x 11 = 121 What is 111 x 111? What is 1,111 x 1,111? What is 111,111,111 x 111,111,111? What is 1,111,111,111 x 1,111,111,111?

No  calculator  is  allowed!  

What  is  a  vector?  

•  A  quanCty  possessing  both  magnitude  and  direcCon,  represented  by  an  arrow  the  direcCon  of  which  indicates  the  direcCon  of  the  quanCty  and  the  length  of  which  is  proporConal  to  the  magnitude.  

Basic  DefiniCon!  

Vector  Data  

(x1, y1)

(x2, y2)

(x4, y4) (x3, y3)

Point  –  pair  of  (x,y)  coordinates  

(x2, y2)

(x1, y1)

(x1, y1)

(x1, y1)

(x1, y1)

(x1, y1)

Line  –  a  sequence  of  points  

Polygon  –  a  closed  set  of  lines  

All  vector  shapes  (2D  and  3D)  are  made  from  a  set  of  points.  

Triangulated  Irregular  Network  Edge

Node

Face

A  vector  is  an  element  of  vector  space  

Vector  Space  of  FuncCons  

Examples  

Examples