This module explains B-splines, which form a basis for splines.
One can look at the operation of a matrix times a vector as changing the basis set for the vector or as changing the vector with the same basis description.
This module derives the Discrete-Time Fourier Series (DTFS), which is a fourier series type expansion for discrete-time, periodic functions. The module also takes some time to review complex sinusoids which will be used as our basis.
This module gives an example on function space.
This module defines generating sets and bases in linear algebra.
Geometric representation of signals provides a compact, alternative characterization of signals.
This module gives an overview of wavelets and their usefulness as a basis in image processing. In particular we look at the properties of the Haar wavelet basis.
This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing.
This module will give a very brief tutorial on some of the basic terms and ideas of linear algebra. These will include linear independence, span, and basis.
B-splines form a simple set of scaling functions satisfying the dilation equation with binomial filter coefficients. However B-Splines other than the zeroth order B-spline (the Haar function) are not orthogonal to its own shifts. Hence to form a perfect reconstruction(PR) filter bank system, biorthogonal scaling functions are used. Also semiorthogonal filter banks can be used to form a PR filter bank system.
In this module we compute bases for the null and column spaces of an adjacency matrix associated with a ladder.
This page explains how to set up our face recognition system for detection. It is centered around the creation of the "eigenface" basis for "face space." It also discusses simplifying the eigenface basis to a level that is both manageable and accurate.
This module defines the terms transpose, inner product, and Hermitian transpose and their use in finding an orthonormal basis.
The module looks at decomposing signals through orthonormal basis expansion to provide an alternative representation. The module presents many examples of solving these problems and looks at them in several spaces and dimensions.
This module defines subspaces, span, linear independence, bases and dimension.
This module discusses the different types of basis that leads up to the definition of an orthonormal basis. Examples are given and the useful of the orthonormal basis is discussed.
This module introduces vector space.
This module introduces real and complex vector spaces, with examples. Notions of linear independence, linear span, basis, dimension, subspaces, and direct sums are covered.
