Create a Matrix



In [28]:

    
A = [1 2 3; 5 6 7; 12 19 22]









    Out[28]:





3x3 Array{Int64,2}:
  1   2   3
  5   6   7
 12  19  22

`'` is the transpose operator

You can use the transpose() method, but using ' is often more convenient



In [29]:

    
A'









    Out[29]:





3x3 Array{Int64,2}:
 1  5  12
 2  6  19
 3  7  22

`⁻¹` is not the inverse operator

There is no inverse operator. Instead you can use the inv() method, or just raise the matrix to the -1th power



In [30]:

    
A^-1









    Out[30]:





3x3 Array{Float64,2}:
 -0.0625   0.8125  -0.25
 -1.625   -0.875    0.5 
  1.4375   0.3125  -0.25

⋅ is the dot product operator

Type \cdot<Tab> to get this operator. You can also call it as a function using dot(A, B)

In Julia 0.4, for multi-dimensional matrices, we need to use the vecdot function instead.



In [31]:

    
vecdot(A', (A^-1))









    Out[31]:





3.000000000000001

Similarly, × is the cross product operator

Type \times<Tab> to get this operator, or use the cross(A, B) function.

The regular rules for matrix multiplication hold.

Vectors

A vector is a special Matrix that has only 1 column. Remember that Julia's arrays are column major, even if they are displayed as a row here (that's just to make a compact display)



In [32]:

    
a = [1 2 3 4 5]
b = [3 5 7 9 11]









    Out[32]:





1x5 Array{Int64,2}:
 3  5  7  9  11

∩ is the Set intersection operator

Type \cap<Tab> to get this operator



In [33]:

    
a ∩ b









    Out[33]:





2-element Array{Int64,1}:
 3
 5

∪ is the Set union operator

Type \cup<Tab> to get this operator



In [34]:

    
a ∪ b









    Out[34]:





8-element Array{Int64,1}:
  1
  2
  3
  4
  5
  7
  9
 11

And there are many more set operators

\in, \ni, \subseteq



In [35]:

    
3 ∈ a









    Out[35]:





true



In [36]:

    
4 ∈ b









    Out[36]:





false



In [37]:

    
b ∋ 3









    Out[37]:





true



In [38]:

    
a ⊆ b









    Out[38]:





false

`hcat` concatenates two arrays horizontally



In [39]:

    
hcat(a, b)









    Out[39]:





1x10 Array{Int64,2}:
 1  2  3  4  5  3  5  7  9  11

`vcat` concatenates two arrays vertically



In [40]:

    
vcat(a, b)









    Out[40]:





2x5 Array{Int64,2}:
 1  2  3  4   5
 3  5  7  9  11

You can also add and subtract two vectors



In [41]:

    
a + b









    Out[41]:





1x5 Array{Int64,2}:
 4  7  10  13  16

Remember that dimensions must match



In [42]:

    
A + a









    



LoadError: DimensionMismatch("dimensions must match")
while loading In[42], in expression starting on line 1

 in promote_shape at operators.jl:220
 in + at arraymath.jl:96

But if one of the operands is a scalar it's okay



In [43]:

    
A * 2









    Out[43]:





3x3 Array{Int64,2}:
  2   4   6
 10  12  14
 24  38  44



In [44]:

    
A + 2









    Out[44]:





3x3 Array{Int64,2}:
  3   4   5
  7   8   9
 14  21  24

Some functions only accept vectors, not arrays

Use the vec() function to turn a generic single dimensional array into a column vector



In [45]:

    
cor(vec(a), vec(b))









    Out[45]:





0.9999999999999998



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