Lecture-4-2-Linear Algebra-slides

Lecture-4-2-Linear Algebra-slides - BME5020 2006 Fall...

Info iconThis preview shows pages 1–10. 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 Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Linear Algebra BME 5020 Computer and Mathematical Application in Bioengineering © 2006 Jingwen Hu September 28, 2006 • Gauss Elimination • LU Decomposition • Matrix Inverse Contents BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Introduction BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University • An equation of the form ax+by+c=0 or equivalently ax+by=-c is called a linear equation in x and y variables. • ax+by+cz=d is a linear equation in three variables, x, y , and z . • Thus, a linear equation in n variables is a 1 x 1 +a 2 x 2 + … +a n x n = b • A solution of such an equation consists of real numbers c 1 , c 2 , c 3 , … , c n . If you need to work more than one linear equations, a system of linear equations must be solved simultaneously. BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Introduction BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University • A system of equations with the form: n n nn n n n n n n b x a x a x a b x a x a x a b x a x a x a = + + + = + + + = + + + ... ... ... ... ... 2 2 1 1 2 2 2 22 1 21 1 1 2 12 1 11 is typically referred to as linear algebraic equations. Frequently, these equations are expressed as [A] {x} = {b} BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Special Matrix • Symmetric matrix: a ij = a ji BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University = 8 7 2 7 3 1 2 1 5 ] [ A BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Special Matrix • Diagonal matrix BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University = 44 33 22 11 ] [ a a a a A BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Special Matrix • Identity matrix BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University = 1 1 1 1 ] [ I BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Special Matrix • Upper triangular matrix BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University = 44 34 33 24 23 22 14 13 12 11 ] [ a a a a a a a a a a A BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Special Matrix • Lower triangular matrix BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University = 44 43 42 41 33 32 31 22 21 11 ] [ a a a a a a a a a a A BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Special Matrix • Banded matrix BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University = 44 43 34 33 32 23 22 21 12 11 ] [ a a a a a a a a a a A BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University...
View Full Document

{[ snackBarMessage ]}

Page1 / 38

Lecture-4-2-Linear Algebra-slides - BME5020 2006 Fall...

This preview shows document pages 1 - 10. Sign up to view the full document.

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