Slides_2010_01_06 - Applied linear algebra and numerical...

Info iconThis preview shows pages 1–8. 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

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight 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: Applied linear algebra and numerical analysis January 06, 2010 - Session 2 Prof. Ulrich Hetmaniuk Department of Applied Mathematics January 6, 2010 Comments Scorelator Accounts Displacement A vector can also be thought of as a displacement. How do we measure the length of a displacement? Column Vectors A vector is an object comprised of a magnitude and a direction. These vectors have equal length and direction. Combining magnitude with direction is the key to extending to higher dimensions. Column Vectors Let m be a positive integer. We denote R m the set of all real m-tuples, i.e. the set of all sequences with m components, each of which is a real number. The standard notation for an element x of R m is the column vector notation: x R m x = x 1 . . . x m . (1) Example We have- 1 3 R 2 , 7 3 R 3 , and 1- 2 / 5- 3 / 5 4 R 4 . Equality of Column Vectors We say that two vectors x and y of R m are equal if they satisfy x = x 1 . . . x m y = y 1 . . . y m , x = y iff x i = y i 1 i m . (2) Example x = iff x i = , 1 i m . Addition of Column Vectors We can define the addition of two vectors x and y of R m : x = x 1 . . . x m y = y 1 . . . y m , x + y = x 1 + y 1 . . . x m + y m . (3) The set R m is closed under addition, meaning that whenever the addition is applied to vectors in R m , we obtain another vector in the same set R m ....
View Full Document

Page1 / 28

Slides_2010_01_06 - Applied linear algebra and numerical...

This preview shows document pages 1 - 8. Sign up to view the full document.

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