A Cluttered Mind

$\newcommand\R{\mathbb{R}}\newcommand\C{\mathbb{C}}\newcommand\Z{\mathbb{Z}}$ The singular value decomposition is usually defined for a matrix. Here, we will show directly that any linear map between inner product spaces has a singular value decomposition. The singular value decomposition of a …

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$\newcommand\R{\mathbb{R}}\newcommand\C{\mathbb{C}}\newcommand\Z{\mathbb{Z}}$ Details to come, but here is the brief version. Let $M$ be a smooth manifold and $B$ be a bundle over $M$. This implies that there is a projection map $\pi: B \rightarrow M$ …