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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…
Jan 25, 2021
Rafiq Islam

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…
Sep 19, 2024
Rafiq Islam

LU Factorization of a Full rank Matrix using Fortran

Data Science
Machine Learning
Computational Mathematics
Algorithmic Complexity
Programming
Computer Science
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Nov 9, 2021
Rafiq Islam

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
Jan 21, 2021
Rafiq Islam

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…
Jul 1, 2024
Rafiq Islam

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…
Feb 23, 2021
Rafiq Islam

Some Linear Algebra Proofs

Linear Algebra
Mathematics
Proof: To prove this, we will use two known properties of matrices.
Jan 24, 2021
Rafiq Islam

বাংলা ভাষায় আমার লেখা || My Blog in Benglali Language

“বাংলায় ব্লগিং করতে পারলে ভালই হতো” এমন ভাবনা থেকেই ঘাটাঘটি শুরু করলাম কিভাবে নিজের ব্লগে বাংলায় লিখতে পারি। বাংলায় মনের ভাব প্রকাশের অসংখ্য মাধ্যম রয়েছে। সামাজিক যোগাযোগের…
Oct 23, 2024
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