2.2.0.0.2 Vectors

The usual way of creating vectors is as follows, using commas (or blanks) and semi-columns:

 
--> v=[2,-3+%i,7]
 v         =
 
!   2.  - 3. + i      7. !
 
--> v'
 ans       =
 
!   2.       !
! - 3. - i   !
!   7.       !
 
--> w=[-3;-3-%i;2]
 w         =
 
! - 3.       !
! - 3. - i   !
!   2.       !
 
--> v'+w
 ans       =
 
! - 1.       !
! - 6. - 2.i !
!   9.       !
 
--> v*w
 ans       =
 
    18.  
 
--> w'.*v
 ans       =
 
! - 6.    8. - 6.i    14. !

Notice that vector elements that are separated by commas (or by blanks) yield row vectors and those separated by semi-colons give column vectors. The empty matrix is [] ; it has zero rows and zero columns. Note also that a single quote is used for transposing a vector (one obtains the complex conjugate for complex entries). Vectors of same dimension can be added and subtracted. The scalar product of a row and column vector is demonstrated above. Element-wise multiplication (.*) and division (./) is also possible as was demonstrated.

Note with the following example the role of the position of the blank:

-->v=[1 +3]
 v  =
 
!   1.    3. !
 
-->w=[1 + 3]
 w  =
 
!   1.    3. !
 
-->w=[1+ 3] 
 w  =
 
    4. 
 
-->u=[1, + 8- 7]
 u  =
 
!   1.    1. !

Vectors of elements which increase or decrease incrementely are constructed as follows

 
--> v=5:-.5:3
 v         =
 
!   5.    4.5    4.    3.5    3. !

The resulting vector begins with the first value and ends with the third value stepping in increments of the second value. When not specified the default increment is one. A constant vector can be created using the ones and zeros facility

 
--> v=[1 5 6]
 v         =
 
!   1.    5.    6. !
 
--> ones(v)
 ans       =
 
!   1.    1.    1. !
 
--> ones(v')
 ans       =
 
!   1. !
!   1. !
!   1. !
 
--> ones(1:4)
 ans       =
 
!   1.    1.    1.    1. !
 
--> 3*ones(1:4)
 ans       =
 
!   3.    3.    3.    3. !

-->zeros(v)
 ans  =
 
!   0.    0.    0. !
 
-->zeros(1:5)
 ans  =
 
!   0.    0.    0.    0.    0. !

Notice that ones or zeros replace its vector argument by a vector of equivalent dimensions filled with ones or zeros.