SVD of compact operator // singular value decomposition
Here, we decompose the singular value decomposition of operators on infinite dimensional spaces. In the case of compact operators, which is a direct extension of the finite-dimensional setting, we replace the sum of outer products of vectors with first-order tensors between Hilbert spaces. Singular value decomposition is the main force of data science, and it turns out that the expansion of infinite-dimensional data points is very simple. Come take a look at your own watch! //Next watch what is the Delta function: The spectral theorem of self-adjoint compact operators: DMD Explanation: Understanding everything from data-SVD: //Books and references Lang’s real number and functional analysis: Pedersen’s analysis Now: Brunton And Kutz: Data-Driving Science and Engineering: //Recording Equipment Canon SL3: Canon T6i: Rode VideoMic: Blue Yeti Microphone: Yeti Nano Microphone: SanDisc 256GB SD Card: Neewer 5600K USB LED Light: Neewer 18-inch Ring Light: Camera Power Adapter: //Music provided by Epidemic Sound Vegas-Onde Norte as I know now-Cacti Place is called home-Jonas Meadows Use this referral link to get a 30-day free trial of Epidemic Sound for your YouTube channel: Disclaimer: This description The above links in may be affiliate links. If you use the provided link to make a purchase, I may receive a small commission, but you will not be charged extra:) Thank you for supporting my channel so that I can continue to make math content for you! //Chaptering 0:00 Start 1:01 Domain Basis 2:38 Range Basis 3:50 SVD of Compact Operators.