Lecture02: Matrices & Transformations

Matrices

Matrices are arrays of numbers arranged in rows and columns. They are fundamental in solving systems of linear equations and performing linear transformations.

Matrix Operations

From addition and subtraction to multiplication and inversion, matrix operations are essential tools in linear algebra.

Linear Transformations

Every matrix represents a linear transformation. These transformations can stretch, shrink, rotate, or reflect vectors in various spaces.

Geometric Interpretation

Understanding the geometric impact of matrices on vectors provides a more intuitive grasp of complex transformations.

Numpy

Numpy is a powerful Python library used extensively for numerical computations.

Introduction to Numpy Arrays

Learn the basics of array creation, manipulation, and operations using Numpy.

Matrix Computations with Numpy

Numpy offers efficient tools for matrix arithmetic, making it an invaluable asset for anyone studying linear algebra.

Dimensions.. Dimensions..

The concept of dimensionality isn’t just about counting rows and columns. It can also refer to the number of independent directions in a space or the number of parameters in a model.

Parallel Computation Principles

In the age of powerful computing, understanding how to run computations in parallel can vastly speed up matrix operations and data processing.

Parallelizing Matrix Operations

Harness the power of parallel computing to process large matrices and datasets.

Dot Product & Cross Product Revised

A revisit to two fundamental vector operations: the dot product and the cross product.

Geometric Significance

Deepen your understanding of these products by visualizing their geometric implications.