This preview shows pages 1–4. Sign up to view the full content.
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 Document
Unformatted text preview: Review of Linear Algebra Chapter 7 of Numerical Methods with MATLAB, Gerald Recktenwald PGE 310: Formulation and Solution in Geosystems Engineering Dr. Balhoff Spring 2011 1 Vector is an ordered set of real (or complex) numbers arranged as a row or column z scalar lowercase Greek ( VDE ) z vector lowercase roman (u,v,x,y,b) z matrix uppercase roman (A,B,C) m x x x x 2 1 > @ n y y y y 2 1 2 Vector Operations z Addition and Subtraction involve corresponding elements of a different vector with the same number of elements z Multiplication by a Scalar involves multiplication of every element by the scalar z Vector Transpose converts row vector to a column vector or vice versa 3 Linear Combination involves scalar multiplication and vector addition w v u E D 1 1 1 1 1 2 2 2 2 2 m m m m m u v u b v w u v u b v w u v u b v w D D D E D 4 Vector Inner Product is an operation between two vectors that have the same number of elements z ALWAYS results in a scalar z MUST be a row vector times a column vector z Can use transpose for two column vectors n i i i y x y x 1 V V > @ 4 4 3 3 2 2 1 1 4 3 2 1 4 3 2 1 y x y x y x y x y y y y x x x x 5 Vector Norms compare the size (magnitude) of a vector z For example, it makes sense that z Unit vector has a magnitude of 1 z Zero vector has a magnitude of 0 z Absolute Value is a measure of magnitude for scalars z Norm is a measure of magnitude for vectors E D !...
View
Full
Document
 Spring '06
 Klaus

Click to edit the document details