Orthogonal Matrices, Equivalences

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Question of Motivation

Introduces orthogonal and symmetric matrices in linear algebra with practical examples.

Rotation: Attitude and Orientation

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

Orthonormal Vectors Properties

Explores the properties of orthonormal vectors in Euclidean space through key equations and demonstrations.

Hilbert Spaces: Orthonormal Systems

Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.

Singular Value Decomposition: Fundamentals and Applications

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.

Vectors: Coordinate Calculations

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Orthogonality and Subspaces

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

Euclidean Isometries: Properties and Applications

Explores the properties and applications of Euclidean isometries in R^2.

Isometries & Orientation: Modern Symmetry

Explores isometries, reflections, rotations, and translations in space, as well as the structure theorem and configurations of planes and lines.

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.