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1.7 Linear Algebra in Infinite Dimensions

In this video, we translate finite-dimensional linear algebra into function space. Vectors become functions, and matrices become operators—but the underlying structure remains the same.

Watch the full series: https://www.youtube.com/playlist?list=PLdMM2W7mxqIYDURvh37jLz8sd8sDjonk5

0:00 Linear algebra vs function space
2:39 Inner product and norm
9:15 Integral operators
14:46 Adjoint operator
20:59 Mercer theorem
34:02 SVD in function space
42:26 Hilbert space perspective

Topics
• Vectors vs functions
• Inner product and norm (L2)
• Integral operators
• Adjoint operator
• Mercer’s theorem
• Singular value decomposition (SVD)
• Hilbert space

Видео 1.7 Linear Algebra in Infinite Dimensions канала Jingyuan Hu
function space L2 space hilbert space infinite dimensional space inner product L2 integral operator adjoint operator spectral theorem mercer theorem singular value decomposition reproducing kernel machine learning theory functional analysis linear operator SVD in function space
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28 февраля 2026 г. 5:03:37
00:45:32
Jingyuan Hu
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