{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

apxD copy

# apxD copy - NUMERICAL MATHEMATICS COMPUTING 6th Edition...

This preview shows pages 1–8. Sign up to view the full content.

NUMERICAL MATHEMATICS & COMPUTING 6th Edition Ward Cheney/David Kincaid c UT Austin Engage Learning: Thomson-Brooks/Cole www.engage.com www.ma.utexas.edu/CNA/NMC6 September 1, 2011 Ward Cheney/David Kincaid c (UT Austin[10pt] Engage Learning: Thomson-Brooks/Cole www.engage.com[10pt] www.ma.utexas.edu/ NUMERICAL MATHEMATICS & COMPUTING 6th Edition September 1, 2011 1 / 48

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

View Full Document
Appendix D. Linear Algebra Concepts and Notation The two concepts from linear algebra that we are most concerned with are vectors matrices Their usefulness is in compressing complicated expressions into a compact notation. Here the vectors and matrices are most often real consisting of real numbers. These concepts easily generalize to complex vectors and matrices. Ward Cheney/David Kincaid c (UT Austin[10pt] Engage Learning: Thomson-Brooks/Cole www.engage.com[10pt] www.ma.utexas.edu/ NUMERICAL MATHEMATICS & COMPUTING 6th Edition September 1, 2011 2 / 48
Vectors A vector x 2 R n can be thought of as a one-dimensional array of numbers written as x = 2 6 6 6 4 x 1 x 2 . . . x n 3 7 7 7 5 where x i is called the i th element , entry , or component . An alternative notation that is useful in pseudocodes is x = ( x i ) n Sometimes the vector x displayed above is said to be a column vector to distinguish it from a row vector y written as y = [ y 1 , y 2 , . . . , y n ] Ward Cheney/David Kincaid c (UT Austin[10pt] Engage Learning: Thomson-Brooks/Cole www.engage.com[10pt] www.ma.utexas.edu/ NUMERICAL MATHEMATICS & COMPUTING 6th Edition September 1, 2011 3 / 48

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

View Full Document
For example, here are some vectors: 2 6 6 6 6 6 4 1 5 3 - 5 6 2 7 3 7 7 7 7 7 5 , [ , e , 5 , - 4] , " 1 2 1 3 # Ward Cheney/David Kincaid c (UT Austin[10pt] Engage Learning: Thomson-Brooks/Cole www.engage.com[10pt] www.ma.utexas.edu/ NUMERICAL MATHEMATICS & COMPUTING 6th Edition September 1, 2011 4 / 48
To save space, a column vector x can be written as a row vector such as x = [ x 1 , x 2 , . . . , x n ] T or x T = [ x 1 , x 2 , . . . , x n ] By adding a T (for transpose ) to indicate that we are interchanging or transposing a row or column vector. As an example, we have [1 2 3 4] T = 2 6 6 4 1 2 3 4 3 7 7 5 Ward Cheney/David Kincaid c (UT Austin[10pt] Engage Learning: Thomson-Brooks/Cole www.engage.com[10pt] www.ma.utexas.edu/ NUMERICAL MATHEMATICS & COMPUTING 6th Edition September 1, 2011 5 / 48

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

View Full Document
Many operations involving vectors are component-by-component operations . For vectors x and y x = 2 6 6 6 4 x 1 x 2 . . . x n 3 7 7 7 5 , y = 2 6 6 6 4 y 1 y 2 . . . y n 3 7 7 7 5 the following definitions apply. Ward Cheney/David Kincaid c (UT Austin[10pt] Engage Learning: Thomson-Brooks/Cole www.engage.com[10pt] www.ma.utexas.edu/ NUMERICAL MATHEMATICS & COMPUTING 6th Edition September 1, 2011 6 / 48
Equality x = y if and only if x i = y i for all i Inequality x < y if and only if x i < y i for all i Addition/Subtraction x ± y = 2 6 6 6 4 x 1 ± y 1 x 2 ± y 2 . . . x n ± y n 3 7 7 7 5 Scalar Product x = 2 6 6 6 4 x 1 x 2 .

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 48

apxD copy - NUMERICAL MATHEMATICS COMPUTING 6th Edition...

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

View Full Document
Ask a homework question - tutors are online