Linear Transformations: Matrices and Applications

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Related lectures (30)

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Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Advanced Physics I

Covers velocity, acceleration, dynamics, moments of inertia, and kinetic energy storage systems.

Symmetries of Navier-Stokes Equations

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

Inertia Tensor: Main Axes and Principal Moments

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Symmetry in the Plane

Explores the modern definition of symmetry and its practical applications.

Isometries: Definition and Examples

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

Linear Applications: Matrices and Transformations

Explores linear applications, matrices, transformations, rotations, symmetries, and properties of applications.

Group Theory: Basics

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Isometries: Transformations Preserving Distances in the Plane

Introduces isometries as transformations preserving distances in the plane, focusing on symmetry and geometric relationships.

Linear Applications: Matrices and Bases

Explores matrices for linear applications, injective and surjective maps, and base transformations.