{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture+6-Linear+Algebra+_+MATLAB+graphics

# Lecture+6-Linear+Algebra+_+MATLAB+graphics - Matrix...

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

Matrix Multiplications Recall how matrix multiplication works g j a b c ag bh ci aj bk cl h k d e f dg eh fi dj ek fl i l g j ga jd gb je gc jf a b c h k ha kd hb ke hc kf d e f i l ia ld ib le ic lf + + + + = + + + + + + + = + + + + + + [A]*[B] A 2 x 3 B 3 x 2 C 2 x 2 =A 2 x 3 *B 3 x 2 B 3 x 2 A 2 x 3 D 3 x 3 =B 3 x 2 *A 2 x 3

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

View Full Document
Matrix multiplication can be performed only if the inner dimensions are equal Matrix Multiplication [A] m x n [B] n x l [C] m x l
Interior dimensions have to be equal For a vector We will be using square matrices (m=n) j i i j k k A B C × × × × = m n n m A x b × × = n n n n b x A = × Matrix Multiplication x n x 1

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

View Full Document
MATLAB In Fortran, the matrix multiplication have to be done by Do Loops In MATLAB, it is automatic A*B = C Note no period (not element-by-element operation) For vectors A*x = b
Matrix Multiplication Associative ( [ A ] [ B ] ) [ C ] = [ A ] ( [ B ] [ C ] ) Distributive [ A ] ( [ B ] + [ C ] ) = [ A ] [ B ] + [ A ] [ C ] ([ A ] + [ B ] ) [ C ] = [ A ] [ C ] + [ B ] [ C ] Not generally commutative [ A ] [ B ] [ B ] [ A ]

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

View Full Document
Matrix Inverse Matrix division is undefined However, there is a matrix inverse for non-singular square matrices [ A ] - 1 [ A ] = [ A ] [ A ] - 1 = [ I ] Matlab: >>inv(A) Multiplication of a matrix by the inverse is analogous to division
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 a a a a a a a a A a

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 / 23

Lecture+6-Linear+Algebra+_+MATLAB+graphics - Matrix...

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

View Full Document
Ask a homework question - tutors are online