Lectures related to Signals & Systems I: Vector Approximation and Signal Comparison

Explores signal approximation, orthogonal bases, Fourier series, correlation, and vector geometry.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

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

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

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

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Explores cross-correlation, convolution, signal approximation, orthonormal functions, and orthogonal approximation theorem in signals and systems.

Covers the fundamental concepts of vectors, including their characteristics and calculation methods.

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

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

Explores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.

Explores cross-correlation, signal detection, Hilbert spaces, orthogonal approximation, and image compression using DCT.

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

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

Introduces orthogonal vectors, scalar product, Euclidean norm, Pythagorean theorem, and unit vectors.

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

Covers landmarks, coordinate systems, frames, and terminology in coordinates, emphasizing geometric angles and orthogonal vectors.

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Covers the decomposition of a vector in a base and its applications in speed and distance calculations.