MATH-111(e): Linear Algebra

Lectures in this course (136)

Covers the proof of the symmetry of a matrix through exercises involving symmetric matrices.

Covers the computation of eigenvalues and eigenvectors of a given matrix.

Covers the spectral theorem, eigenvalues, eigenvectors, and their importance in linear algebra.

Introduces systems and linear equations, defining lines and planes in 2D and 3D spaces.

Explores properties and applications of matrix operations, including invertibility.

Covers the resolution of linear systems, matrix operations, echelon forms, and reduced echelon forms.

Demonstrates the proof of a matrix as a projection matrix in Rn.

Covers matrix product, inverses, and properties of invertible matrices.

Focuses on proving the uniqueness of the zero vector in the kernel of a symmetric matrix.

Covers calculations and algorithms for determining the determinant of a matrix, including permuting rows and multiplying by coefficients.

Covers the process of determining if a matrix is diagonalizable.

Focuses on matrix operations, specifically Exercise 13, covering addition, multiplication, and determinants with detailed examples.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Covers LU decomposition and change of basis for linear transformations.

Explains eigenvalues and eigenvectors of symmetric matrices and their properties.

Covers linear independence, bases, change of basis, and vector representation.

Explains eigenvalues and eigenvectors, focusing on real solutions and their properties.

Explores base changes, bijective linear applications, matrix transformations, and dimensions of kernel and image spaces.

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Page 6 of 7