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### A linear algebra view of the wavelet transform this web page was written to provide some background explaining the structure of wavelet algorithms covered on companion web pages.

Linear algebra and its applications strang. Emphasis is given to topics that will be useful in other disciplines including systems of equations vector spaces determinants eigenvalues similarity and positive definite matrices. Renowned professor and author gilbert strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. Originally utilized to study principal axes of the rotational motion of rigid bodies eigenvalues and eigenvectors have a wide range of applications for example in stability analysis vibration analysis. In mathematics and more specifically in linear algebra and functional analysis the kernel also known as null space or nullspace of a linear map l. V w between two vector spaces v and w is the set of all elements v of v for which lv 0 where 0 denotes the zero vector in wthat is in set builder notation.

This is a basic subject on matrix theory and linear algebra.

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