In this lecture on Change of Basis, Image Compression, and Transformation, the focus is on how change of basis is used in real-world applications. The example of image compression is used to demonstrate how choosing a better basis can save a lot of space while still preserving the integrity of the image. The lecture goes on to explain how the matrix used to describe a linear transformation with respect to coordinates is connected to the linear transformation itself. The Fourier basis is also introduced as the best-known basis for image compression, and the use of wavelets as a competing basis is briefly mentioned.
Change of Basis, Image Compression, and Transformation -- Lecture 31. Applications of change of basis in matrices.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
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Questions answered by this video:
How are images compressed?
How are videos compressed?
What is a change of basis in Linear Algebra?
How are matrices used to compress images?
What are transformation matrices?
What is a Fourier basis?
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A good video explanation of some applications of change of basis of matrices. Some applications include transformations and matrices that describe these transformations and image and video compression techniques using matrices.