Math for Data Science — Lecture 01 Basic Matrix Operations via Python

In this lecture, we will study Matrix Operations (Initialization, Vector, Multiplication, Transpose, Special Matrix) via Python.

Matrix Definition

Image 01: Matrix Definition

Matrix Notation

Image 02: Matrix Notation

Matrix Initialization

import numpy as np
print(np.random.randint(low = 5,high=12, size=(2, 3)))
A = np.matrix([[1, 2], [3, 4], [5,6]])
print("Type of Matrix A:{}, having {} rows and {} columns".format(type(A),A.shape[0],A.shape[1]))
Image 03: Matrix Initialization — code


Image 04: Vector Definition
  • Row vector is having 1 row and N columns
  • Column vector is having N rows and 1 column
Image 05: Row and Column Vector — code
Image 06: Convert Row vector to Column Vector — code

Matrix Equality

Image 07: Check Matrix Equality — code

Matrix Multiplication

Image 08: Matrix Multiplication Shape

In below Image 09, matrix multiplication is shown both via python code and hand as well.

Image 09: Matrix Multiplication calculation by hand
  • Matrix multiplication isn’t commutative (AB != BA)
Image 10: Matrix Not Commutative — code

Matrix Transpose

Image 11: Matrix Transpose — code

Rules of Matrix Transpose

Image 12.1: Rules of Matrix transpose — code
Image 12.2: Rules of Matrix transpose — code

Special Matrix

Image 13: Special Matrices Definition
Image 14: Check if Special Matrix — code
Image 15: Caller Function (Special Matrix) — code

Reduce size of Sparse Matrix using CSR (Compressed Sparse Row)

Image 16: Dense and Sparse Matrix storage comparison — code

Properties of Determinants

Image 17: Properties of Determinants

WORK IN PROGRESS !! Jupyter Notebook/.py will be uploaded soon..

Our Next lecture is about using Elementary row operations to find Row Echelon Form (REF), Reduced Row Echelon Form (RREF) and Rank of Matrix (

Meanwhile, Please feel free to clap if you liked the article. Also, please subscribe to my YouTube Channel




Idea is to understand math for data science from intuition and code (mainly python)

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Aakash Goel

Aakash Goel

Senior Data Scientist @ Fractal Analytics

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