Understanding Wave Dualism, Commutation Relations, and Orthogonality Principle
Explore the concepts of wave dualism, commutation relations, and the orthogonality principle in vector spaces. Discover how vectors can be expressed, approximated, and optimized within different subspaces. Dive into the mathematical foundations behind these principles through informative slides.
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Presentation Transcript
Orthogonality Principle As discussed previously, any vector in a vector space can be expressed as a linear combination of the basis vectors that span the space. Here we will consider how the vector can be optimally approximated in a subspace spanned by a subset of the basis vectors. Specifically we assume a given function in the function space is approximated in a subspace by
