Examine the properties and significance of orthogonal matrices, including definitions, transpose-inverse relationships, and their role in preserving lengths and angles. This episode highlights applications in numerical methods, coordinate transformations, and stability analysis, with clear examples to support conceptual understanding.

Learn the fundamentals of the eigenvalue problem, including how to find eigenvalues and eigenvectors, their geometric interpretation, and their role in solving systems of linear equations and differential equations. This episode provides step-by-step examples and highlights key applications in engineering analysis, control systems, and vibrations.

Delve into the core concepts of vector spaces, including definitions, subspaces, basis, dimension, and spanning sets. This episode explains how vector spaces form the backbone of linear algebra and why they matter in engineering applications. Ideal for revising key ideas, reinforcing lecture content, and preparing for exams with structured, example-based learning.

Explore the fundamentals of Laplace transforms, a powerful tool for solving differential equations in engineering. This episode covers the basic definition, key properties, common transforms, and practical applications in system analysis. Ideal for reinforcing concepts from lectures and textbooks, with clear examples to support understanding and exam prep.

In this episode, we break down two powerful concepts in linear algebra: matrix diagonalisation and quadratic forms. Whether you're brushing up for an exam or just curious about how these ideas shape the math behind engineering, physics, and data science, we've got you covered.

We'll explore:

🔹 What it means to diagonalise a matrix and why it's useful

🔹 The role of eigenvalues and eigenvectors

🔹 How to simplify quadratic forms using orthogonal diagonalisation