Matrices and arrays

The Julia programming language provides extensive capabilities for creating and editing matrices. In this example, some of them will be considered.

To create a matrix consisting of several rows, separate the elements of the matrix with a semicolon:

a = [1 3 5; 2 4 6; 7 8 10]

3×3 Matrix{Int64}:
 1  3   5
 2  4   6
 7  8  10

Julia allows you to process all the values in a matrix using a single arithmetic operator or function by specifying a dot in front of it, which means applying the operator element-by-element.:

a .+ 10

3×3 Matrix{Int64}:
 11  13  15
 12  14  16
 17  18  20

Piecemeal exponentiation:

a .^ 3

3×3 Matrix{Int64}:
   1   27   125
   8   64   216
 343  512  1000

You can also apply functions to matrices:

sin(a)

3×3 Matrix{Float64}:
 -0.657343  -0.275398   0.014688
 -0.572697  -0.24759   -0.144781
  0.254022  -0.38759   -0.874514

The matrix can be transposed in two ways, the first is by specifying an apostrophe.:

a'

3×3 adjoint(::Matrix{Int64}) with eltype Int64:
 1  2   7
 3  4   8
 5  6  10

The second way is to use the transpose function:

transpose(a)

3×3 transpose(::Matrix{Int64}) with eltype Int64:
 1  2   7
 3  4   8
 5  6  10

Matrices are concatenated when they are indicated in square brackets, separated by semicolons or without them, which means, respectively, vertical and horizontal addition.:

A = [a; a]

6×3 Matrix{Int64}:
 1  3   5
 2  4   6
 7  8  10
 1  3   5
 2  4   6
 7  8  10

Concatenation of matrices horizontally:

A = [a a]

3×6 Matrix{Int64}:
 1  3   5  1  3   5
 2  4   6  2  4   6
 7  8  10  7  8  10

You can also use complex numbers as array elements by defining them using im:

c = [3+4im 4+3im; -im 10im]

2×2 Matrix{Complex{Int64}}:
 3+4im  4+3im
 0-1im  0+10im