Matrices and Orthogonal Transformations

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Related lectures (31)

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Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Vector Calculus in 3D

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Vector Spaces: Properties and Examples

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Vector Spaces: Basics

Covers the basics of vector spaces, including operational definitions, properties, examples in RN, inner products, norms, and distances.

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Orthogonality and Subspaces

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

Orthogonality and Scalar Product

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Real Vector Space: Basics

Introduces the basics of real vector spaces, norms, and scalar products.

Isometries: Definition and Examples

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Symmetries of Navier-Stokes Equations

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.