Lecture1 - University of Toronto at Scarborough Department...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A23 Winter 2008 Lecture 1 Sophie Chrysostomou Definition : If n is a positive integer, the Euclidean n-space, R n , is the collection of all ordered n-tuples of real numbers. There are two types of n-tuples in R n : ( a 1 , a 2 , , a n ) [ a 1 , a 2 , , a n ] The zero vector in R n is the vector containing zeroes in all of its compo- nents: = [0 , , , 0]. Geometric Interpretation of Vectors. In R In R 2 : In R 3 1 We can generalize and say that the vector a = [ a 1 , a 2 , , a n ], in its standard position, is the arrow that starts at the origin (0 , , , 0) and ends at the point ( a 1 , a 2 , , a n ) . A vector of the same length and direction as a , is the vector a translated to another position in R n . For this reason it is also called a . Vector Algebra in R n : Let v = [ v 1 , v 2 , , v n ] and w = [ w 1 , w 2 , , w n ] be in...
View Full Document

Page1 / 5

Lecture1 - University of Toronto at Scarborough Department...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online