Vector_matrices

Vector_matrices - Vectors and Matrices Linear equations can...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Vectors and Matrices • Linear equations can be conveniently represented using matrices and vectors • A vector is an ordered list of numbers • A matrix is a rectangular array of numbers
Background image of page 1

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

View Full DocumentRight Arrow Icon
Matrices • The set of (m x n) real matrices is noted • Example
Background image of page 2
Matrix arithmetic • Addition is done element by element • Example in • Addition is commutative: A+B=B+A
Background image of page 3

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

View Full DocumentRight Arrow Icon
Matrix multiplication • Matrix multiplication is defined by • The dimensions of A and B must be compatible
Background image of page 4
Matrix multiplication • Example with i th row of A j th column of B
Background image of page 5

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

View Full DocumentRight Arrow Icon
Matrix multiplication • Example
Background image of page 6
Matrix multiplication • Matrix multiplication is not commutative • Even if A*B is defined, B*A may not be defined – If A and B have compatible dimensions, this does not mean that B and A have compatible dimensions – Example:
Background image of page 7

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

View Full DocumentRight Arrow Icon
Matrix transposition • The transpose A T of a matrix A is defined by • Example
Background image of page 8
Vectors • A column vector in is an ordered list of m numbers • Example: m=4
Background image of page 9

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

View Full DocumentRight Arrow Icon
Vectors • A row vector in is a (1 x n) matrix • If x is a column vector, its transpose x T is a row vector
Background image of page 10
• Addition is done term by term • Example
Background image of page 11

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

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/06/2011 for the course CHE 110A taught by Professor Mccurdy during the Fall '09 term at UC Davis.

Page1 / 21

Vector_matrices - Vectors and Matrices Linear equations can...

This preview shows document pages 1 - 12. Sign up to view the full document.

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