This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full 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 mtuples, 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
 Winter '07
 Leveque
 Linear Algebra, Numerical Analysis, Vector Space, Dot Product, Euclidean space

Click to edit the document details