MATH-111(e): Linear Algebra

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Lectures in this course (136)

Determinants and Row Echelon Form

Covers determinants, row echelon form, properties, and geometric interpretation of determinants.

Eigenvalue Geometric Multiplicity

Explains how to determine the geometric multiplicity of an eigenvalue in a matrix.

Linear Equations: Solutions and Operations

Covers the solution of linear equations and operations with matrices and vectors.

Diagonalization of Matrices and Least Squares

Explores diagonalization of matrices, similarity relations, and eigenvectors in linear algebra.

Matrix multiplication: understanding the associativity property

Explores the implications of matrix multiplication resulting in zero and emphasizes the importance of understanding matrix operations.

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Singular Value Decomposition (SVD)

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

Orthogonality and Projections

Demonstrates computing inner products and projections between vectors in a given space.

Eigenvalues and Eigenvectors: Understanding Matrix Transformations

Explores eigenvalues and eigenvectors in matrix transformations, essential for understanding mathematical and real-world systems.

Matrix Invertibility

Covers the proof of the invertibility of a matrix by showing that the transpose of the matrix multiplied by itself results in an identity matrix.

Vector Spaces: Basics and Operations

Covers the basics of vector spaces, including addition, scalar multiplication, and zero vectors, with examples and applications.

Eigenvalues and Eigenvectors: Understanding Matrix Properties

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Linear Algebra: Orthogonal Vectors

Explores orthogonal vectors in linear algebra and their significance in calculations and applications.

Eigenvalues and Eigenvectors: Polynomials and Matrices

Explores eigenvalues, eigenvectors, and characteristic polynomials of matrices, emphasizing their importance in matrix operations.

Vector Spaces: Examples and Subspaces

Covers examples of vector spaces and the concept of subspaces, emphasizing key properties and verification methods.

Linear Systems Resolution: Echelon & Reduced Echelon Forms

Explains echelon and reduced echelon forms of matrices and the pivot method for solving linear systems.

Eigenvalues and Diagonalization

Explores eigenvalues, diagonalization, and matrix similarity, showcasing their importance and applications.

Orthogonal Basis of Subspaces

Explains the concept and calculations of orthogonal bases for subspaces in linear algebra.

Diagonalization: Theory and Examples

Explores diagonalization of matrices through eigenvalues and eigenvectors, emphasizing distinct eigenvalues and their role in the diagonalization process.

Least Squares Solution to Ax=b

Covers the least squares solution to the equation Ax=b, focusing on the normal equation and its application.

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