The Idea of Elimination
Elimination is a foundational technique in linear algebra. It’s used primarily to simplify systems of equations and reveal their fundamental structure.
Understanding Gaussian Elimination
A step-by-step walkthrough of the Gaussian elimination method. We’ll cover how to use elementary row operations to transform a matrix to its echelon form.
Rules for Matrix Operations
Matrix operations are at the heart of many mathematical, engineering, and computational applications. We’ll delve deep into the rules governing these operations.
Addition and Subtraction
Discover the essentials of matrix addition and subtraction, including conformability and resulting matrix dimensions.
Matrix Multiplication
A closer look at matrix multiplication, exploring its non-commutative nature and its applications in transformations.
Inverse Matrices
Inverse matrices play a crucial role in solving linear systems, among other applications.
Properties and Significance
Learn the properties an inverse matrix must satisfy and why they’re so crucial for matrix algebra.
Calculating the Inverse
A hands-on guide on how to compute the inverse of a matrix using elementary row operations and determinants.
Permutations
Permutations are about arrangement. In the context of matrices, they become particularly interesting.
Significance in Matrix Algebra
How do permutations relate to matrices? Explore their role in determining matrix properties, especially the determinant.
Permuting Rows and Columns
A dive into practical applications: when and why would we want to permute rows or columns in a matrix?
Lecture03: Matrices & Views & Numpy
