Example:
x = np.array([1, 2, 3])
output = make_diagonal(x)
print(output)
# Output:
# [[1. 0. 0.]
# [0. 2. 0.]
# [0. 0. 3.]]
Reasoning:
The input vector [1, 2, 3] is converted into a diagonal matrix where the elements of the vector form the diagonal of the matrix.
A diagonal matrix is a square matrix in which the entries outside the main diagonal are all zero. The main diagonal is the set of entries extending from the top left to the bottom right of the matrix.
In this problem, you will write a function to convert a 1D numpy array (vector) into a diagonal matrix. The resulting matrix will have the elements of the input vector on its main diagonal, and zeros elsewhere.
Given a vector \( \mathbf{x} = [x_1, x_2, \ldots, x_n] \), the corresponding diagonal matrix \( \mathbf{D} \) is:
\[ \mathbf{D} = \begin{bmatrix} x_1 & 0 & 0 & \cdots & 0 \\ 0 & x_2 & 0 & \cdots & 0 \\ 0 & 0 & x_3 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & x_n \end{bmatrix} \]Diagonal matrices are important in various mathematical and scientific computations because of their simple structure and properties.
import numpy as np
def make_diagonal(x):
identity_matrix = np.identity(np.size(x))
return (identity_matrix*x)
There’s no video solution available yet 😔, but you can be the first to submit one at: GitHub link.