channelflow.org

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.

====== Math 445 lecture 2: Vectors ======

===== Vectors in math =====

Vectors are hugely important in math, science, engineering.
In math, a vector is a list of numbers. E.g. this is a 3-d vector 

<latex>
  v = \left(\begin{array}{c} 4.3 \\ 5.9 \\ 0.1 \end{array} \right)
</latex>


In math, the components or elements of a vector are written with subscripts.
E.g. for the above vector

<latex>
 v_1 = 4.3, \quad v_2 = 5.9, \quad v_3 = 0.1
</latex>

===== Creating vectors with explicit lists =====
In Matlab, there's a distinction between row vector and column vectors.
You can construct **row vectors** by listing elements between **square brackets**, 
with either **spaces** or **commas** between.

<code>
>> v = [4.3 5.9 0.1]  % assign a row vector into variable v

v =

    4.3000    5.9000    0.1000 
</code>


To create a column vectors, put semicolons between the elements.

<code>
 >> v = [4.3; 5.9; 0.1] % assign a col vector into variable v

v =

    4.3000
    5.9000
    0.1000
</code>

===== The transpose operator =====

Note that last method. In Matlab, the apostrophe '' ' '' stands for the **transpose**.
The transpose operator turns a row vector into a column vector, and vice versa.


<code>
>> v = [4.3 5.9 0.1]

v =

    4.3000    5.9000    0.1000

>> v'

ans =

    4.3000
    5.9000
    0.1000

>> u = v'

u =

    4.3000
    5.9000
    0.1000

>> w = u'

w =

    4.3000    5.9000    0.1000

</code>

channelflow.org

User Tools

Site Tools

Page Tools