Linear Algebra

Explore the fundamental concepts of vectors, vector spaces, spans, and bases, critical for understanding multidimensional spaces.

Dive into the properties and operations involving matrices, including matrix multiplication, inversion, and determinants.

Learn how to solve systems of linear equations using methods like Gaussian elimination, matrix operations, and Cramer's rule.

Understand how eigenvalues and eigenvectors are found and their significance in simplifying matrix operations and systems of linear equations.

Examine the principles of orthogonal and orthonormal vectors and their applications in simplifying complex vector spaces.

Study the mapping between vector spaces that preserves vector addition and scalar multiplication, and their matrix representation.

Delve into spaces with an additional structure that allows measurement of angles and lengths, central to functional analysis.

Explore the method of orthonormalizing a set of vectors in an inner product space, fundamental in numerical analysis.

Investigate the scalar values that are a measure of the transformation described by a matrix, used in solving linear equations.

Learn about the functions that assign a strictly positive length or size to each vector in a vector space.

Understand the concept of linear independence, a set of vectors that do not linearly rely on each other and its importance in linear algebra.

Examine how the rank of a matrix is determined and its role in understanding the solutions of linear systems.

Study the transition between two different bases for a vector space and its effects on the coordinate representation of vectors.

Discover the mathematical method for determining the best outcome in a mathematical model with linear relationships.

Dive into algorithms and numerical methods for solving linear algebra problems, crucial in computer simulations and data analysis.

Explore the algebraic framework with multi-dimensional arrays of numbers, extending the concepts of scalars, vectors, and matrices.