Manipulating matrices in Julia

• Transpose of a matrix
• Flipping a matrix
• Concatenating matrices
• Reshaping a matrix
• Inverse of a matrix

Creating a matrix

Transpose of a matrix

• The transpose operation flips the matrix over its diagonal by switching the rows and columns.
• Let A be a matrix. We can get the transpose of A by using A'.
Example 1: Python3 1==

# Defining a square matrix of size (2, 2)
A = [1 2; 3 4]    

# Transpose of A 
A'               

Output: Example 2: Python3 1==

# Defining a retangular matrix of size (2, 3)
B = [1 2 3; 4 5 6]   

# Transpose of B
B'                   

Output:

Flipping a matrix:

• A matrix in Julia can be flipped via the X-axis i.e. horizontally or via the Y-axis i.e. vertically.
• To flip the matrix we use reverse(< matrix >, dims= < 1 or 2 >)) 1 = vertically, 2 = horizontally.

# Defining a rectangular matrix of size (2, 3)
B = [1 2 3; 4 5 6]    

# Flipping the matrix vertically
reverse(B, dims = 1)   

# Flipping the matrix horizontally
reverse(B, dims = 2)   

Concatenating matrices

• In Julia we can concatenate a matrix to another matrix to the right side of the initial matrix or to the bottom of it.
• We use vcat(A, B) to concatenate to the side.
• And hcat(A, B) to concatenate to the bottom.
• While concatenating to the side, we need to make sure that both the matrices have same number of rows.
• While concatenating to the bottom, we need to make sure that both the matrices have same number of columns.

# Creating a square matrix of size (2, 2)
A = [1 2; 3 4]        

# Creating a rectangular matrix of size (2, 3)
B = [5 6 7; 8 9 10]   
hcat(A, B)

# Creating a square matrix of size (3, 2)
A = [1 2;3 4; 5 6]        

# Creating a rectangular matrix of size (4, 2)
B = [5 7;8 9; 10 11;14 16]   
vcat(A, B)

Reshaping a matrix

# The original matrix with size (3, 2)
A = [1 2; 3 4; 5 6]    

reshape(A, (2, 3))

reshape(A, (6, 1))

reshape(A, (1, 6))

Inverse of a matrix

• If A is a square matrix its multiplicative inverse is called its inverse matrix. Denoted by A^-1.
• In Julia we use inv(A) to get the inverse of the matrix A.
Example 1: Getting the Inverse of a matrix Python3 1==

# Creating a square matrix of size (2, 2)
A = [4 7; 2 6]      

# Getting the inverse of matrix A  
inv(A)               

Example 2: Getting Identity Matrix Python3 1==

# Creating a square matrix of size (2, 2)
A = [4 7; 2 6]     

# Getting the Identity matrix
A * inv(A)         




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Manipulating matrices in Julia

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Article Tags :

• Julia
• Julia-matrix