Lectures related to Advanced Physics I: Kinetic Energy

Introduces eigenspaces in linear algebra through definitions and practical examples of determining eigenspaces for matrices.

Explores the Eigen library for linear algebra, covering vectors, matrices, arrays, memory management, reshaping, and per-component operations.

Explores advanced physics topics, emphasizing kinetic energy and practical examples.

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Introduces Matlab basics, error handling, and billiards project concepts.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Covers the concept of expressing vectors in proper bases and the importance of diagonalization of matrices.

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Covers rotation matrices and transformations in mathematics, providing examples of rotating vectors in different dimensions.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Covers the basics of programming in Matlab, focusing on interactive usage, mathematical operations, vectors, matrices, strings, and 3D matrices.

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Introduces vector definitions, displacement, addition, and applications in geometry.

Introduces scalars and vectors, explaining their properties and mathematical operations.

Explores properties and interpretations of vectors in space, including mixed product and linear dependence.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

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

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.