SUNY Geneseo Department of Mathematics

Introduction to Vectors

Monday, September 21

Math 230 01
Fall 2015
Prof. Doug Baldwin

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Misc
- Colloquium
  - “Suspect Something Fishy? How Statistics Can Help Detect It, Quickly!”
  - Dr. Aleksey Polunchenko, SUNY Binghamton
  - Wednesday, Sept. 23, 2:45
  - Newton 204
  - Extra credit for short write-ups, like last colloquium
Questions?

Vectors

Sections 5.1 - 5.4
- Definition: ordered list of numbers
  - aka row array
- Enclose vector in square brackets []
  - Row: separate numbers with commas
  - Column: separate numbers with semicolons
- Other ways to create vectors
  - Double colon
  - linspace function
  - logspace function (base ten)
- Pick an element out of vector using parentheses around index

Examples

Create a vector containing the numbers of computers each person in the back row has with them now
- 2, 3, 3, 4, 2, 5
```
>> computers = [ 2 3 3 4 2 5 ]
computers =
     2     3     3     4     2     5
```
Generate a new vector containing 2 times each number in the number-of-computers vector
```
>> moreComputers = computers * 2
moreComputers =
     4     6     6     8     4    10
```

Create a vector containing the integers 2 through 7

>> [ 2 : 7 ]
ans =
     2     3     4     5     6     7
>> [ 2 : 1/3 : 7 ]
ans =
  Columns 1 through 4
    2.0000    2.3333    2.6667    3.0000
  Columns 5 through 8
    3.3333    3.6667    4.0000    4.3333
  Columns 9 through 12
    4.6667    5.0000    5.3333    5.6667
  Columns 13 through 16
    6.0000    6.3333    6.6667    7.0000

Create a vector containing 1000 numbers equally spaced between 0 and π (inclusive)

>> nums = linspace( 0, pi, 1000 )
nums =
  Columns 1 through 4
    0    0.0031    0.0063    0.0094
  …
  Columns 997 through 1000
    3.1322    3.1353    3.1384    3.1416
>> nums( 500 )
ans =
    1.5692

Create a vector containing as many 0s as there are people in this room

>> linspace( 0, 0, 23 )
ans =
  Columns 1 through 7
     0     0     0     0     0     0     0
  Columns 8 through 14
     0     0     0     0     0     0     0
  Columns 15 through 21
     0     0     0     0     0     0     0
  Columns 22 through 23
     0     0
>> 0 * [1:23]
ans =
  Columns 1 through 7
     0     0     0     0     0     0     0
  Columns 8 through 14
     0     0     0     0     0     0     0
  Columns 15 through 21
     0     0     0     0     0     0     0
  Columns 22 through 23
     0     0
>> zeros( 1, 23 )
ans =
  Columns 1 through 7
     0     0     0     0     0     0     0
  Columns 8 through 14
     0     0     0     0     0     0     0
  Columns 15 through 21
     0     0     0     0     0     0     0
  Columns 22 through 23
     0     0
% Some other vectors and matrices of constants
>> ones( 1, 23 )
ans =
  Columns 1 through 7
     1     1     1     1     1     1     1
  Columns 8 through 14
     1     1     1     1     1     1     1
  Columns 15 through 21
     1     1     1     1     1     1     1
  Columns 22 through 23
     1     1
>> eye( 3 )
ans =
     1     0     0
     0     1     0
     0     0     1
>> 49 * ones( 1, 23 )
ans =
  Columns 1 through 7
    49    49    49    49    49    49    49
  Columns 8 through 14
    49    49    49    49    49    49    49
  Columns 15 through 21
    49    49    49    49    49    49    49
  Columns 22 through 23
    49    49

Create a vector containing the first 16 powers of 2 (i.e., 2¹ through 2¹⁶)

>> % powers of 10 from 10^1 to 10^5
>> logspace( 1, 5, 5 )
ans =
  Columns 1 through 3
          10         100        1000
  Columns 4 through 5
       10000      100000
>> % powers of 2 from 2^1 to 2^16
>> logspace( log10(2), 16*log10(2), 16 )
ans =
   1.0e+04 *
  Columns 1 through 4
    0.0002    0.0004    0.0008    0.0016
  Columns 5 through 8
    0.0032    0.0064    0.0128    0.0256
  Columns 9 through 12
    0.0512    0.1024    0.2048    0.4096
  Columns 13 through 16
    0.8192    1.6384    3.2768    6.5536

Vector Lab
- Handout

Next
- Calculating with vectors
- Read sections 5.5 - 5.6 in textbook
- Optionally, “The Dot Operator” video at http://www.see.ed.ac.uk/teaching/courses/matlab/unit01/dot-operator.shtml

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