Introduction to Matrix Operations in Matlab
Introduction to Matrix Operations in Matlab
Gerald W. Recktenwald
Department of Mechanical Engineering
Portland State University
gerry@pdx.edu
ME 350: Introduction to Matrix Operations in Matlab
Overview
Working with Matrices and Vectors
? Linear algebra
? Vectorized operations
? Array operators
ME 350: Introduction to Matrix Operations in Matlab
page 1
Manipulation of Matrices and Vectors
The name ¡°Matlab¡± evolved as an abbreviation of ¡°MATrix LABoratory¡±. The data
types and syntax used by Matlab make it easy to perform the standard operations of
linear algebra including addition and subtraction, multiplication of vectors and matrices,
and solving linear systems of equations.
Later we will review linear algebra. Here we provide a simple introduction to some
operations that are necessary for routine calculation.
?
?
?
?
Vector addition and subtraction
Inner and outer products
Vectorization
Array operators
ME 350: Introduction to Matrix Operations in Matlab
page 2
Vector Addition and Subtraction
Vector and addition and subtraction are element-by-element operations.
Example:
>> u = [10 9 8];
>> v = [1 2 3];
>> u+v
ans =
11
11
11
>> u-v
ans =
9
7
(u and v are row vectors)
5
ME 350: Introduction to Matrix Operations in Matlab
page 3
Vector Inner and Outer Products
The inner product combines two vectors to form a scalar
X
T
¦Ò = u ¡¤ v = u v ?? ¦Ò =
ui vi
The outer product combines two vectors to form a matrix
T
A = u v ?? ai,j = ui vj
ME 350: Introduction to Matrix Operations in Matlab
page 4
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