Lectures related to Navigation Equations: Part 1

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Diagonalisation of Symmetric Matrix by Orthogonal Matrix

Covers the method of diagonalizing a symmetric matrix using an orthogonal matrix.

Diagonalization of Symmetric Matrices

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

Orthogonal Matrices & Spectral Decomposition

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Matrix Multiplication: Applications and Properties

Covers matrix multiplication, properties, and inverses in linear algebra.

Diagonalization of Symmetric Matrices

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

Matrix Decomposition: Triangular and Spectral

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Diagonalization in Symmetric Matrices

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

Orthogonal Base Change

Explores orthogonal base change in linear algebra, focusing on matrices and transformations.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Rotation: Attitude and Orientation

Covers attitude and orientation in rotations, including small angles and orthonormal properties.

Symmetric and Anti-symmetric Matrices

Introduces symmetric and anti-symmetric matrices, matrix powers, inverses, elementary matrices, and matrix manipulation.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Quadratic Forms in IR³

Explores quadratic forms in IR³, matrix properties, diagonalization, and positive definite matrices.