Mathematics

Linear algebra, numerical methods, optimization, and mathematical modeling.

Implementation of Gradient Descent (GD) and Stochastic Gradient Descent (SGD)

Data Science
Machine Learning
Stochastic Gradient Descent
Optimization

GIF Credit: gbhat.com

Gradient Descent is an optimization algorithm used to minimize the cost function. The cost function \(f(\beta)\) measures how well a model with…


September 19, 2024
13 min

Matrix multiplication: Let’s make it less expensive!

Data Science
Machine Learning
Computational Mathematics
Algorithmic Complexity
Have you ever wondered why your code takes forever to run? Sometimes a simple code may take significant time because of an inefficient implementation approach. Let’s take a…
July 1, 2024
6 min

LU Factorization of a Full rank Matrix using Fortran

Data Science
Machine Learning
Computational Mathematics
Algorithmic Complexity
Programming
Computer Science
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November 9, 2021
26 min

Modeling viral disease

Applied Mathematics
Math Biology
Mathematical Modeling
Consider the spreading of a highly communicable disease on an isolated island with population size \(N\). A portion of the population travels abroad and returns to the…
February 23, 2021
3 min

Generalized eigenvectors and eigenspaces

Linear Algebra
Mathematics
Definition: Let \(\alpha\in End(V)\) and \(\lambda\in spec(\alpha)\). A non-zero vector \(v\) is called a generalized eigenvector vector of \(\alpha\) associated with \(\lam…
January 25, 2021
2 min

Some Linear Algebra Proofs

Linear Algebra
Mathematics
Proof: To prove this, we will use two known properties of matrices.
January 24, 2021
5 min

Matrix Representation: Change of Basis

Linear Algebra
Mathematics
Let \(\alpha: \mathcal{P}_2(\mathbb{R}) \longrightarrow M_{2\times 2}(\mathbb{R})\) be defined by
January 21, 2021
3 min
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