MATH-111(g): Linear Algebra

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Lectures in this course (57)

Eigenvalues and Eigenvectors

Covers eigenvalues, eigenvectors, characteristic polynomials, and eigenspaces for square matrices.

Diagonalization of Matrices

Explores the diagonalization of matrices through similarity transformations and the significance of this process in linear algebra.

Eigenvalues and Diagonalization

Explores eigenvalues, eigenvectors, and matrix diagonalization with examples and proofs.

Diagonalization of Matrices

Explores the method of diagonalization for matrices and the calculation of matrix powers.

Orthogonality and Least Squares Method

Introduces orthogonal vectors, scalar product, Euclidean norm, Pythagorean theorem, and unit vectors.

Orthogonality and Subspaces

Explores orthogonality, vector norms, and subspaces in Euclidean space, including determining orthogonal complements and properties of subspaces and matrices.

Matrix Operations and Orthogonality

Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.

Orthogonal Bases in Vector Spaces

Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.

Orthogonal Projection: Theory and Applications

Covers the theory of orthogonal projection in vector spaces and its practical applications.

Orthogonalization of Vectors

Covers the Gram-Schmidt orthogonalization process and vector projections in a vector space.

Orthogonal Projection: Spectral Decomposition

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

QR Factorization: Orthogonal Bases and Matrices

Explores QR factorization, orthogonal bases, and matrices for numerical computations and solving systems of equations.

Orthogonal Matrices and Least Squares Method

Introduces orthogonal matrices, the least squares method, and their practical applications in linear algebra.

Least Squares Solutions

Covers least squares solutions for linear systems using matrix operations and normal systems, illustrated with examples.

Diagonalization of Symmetric Matrices

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Matrix Operations: LU Factorization & Linear Independence

Covers LU factorization, linear independence, and matrix equations.

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