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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

2 votes
1 answer
227 views

Average the covariance matrix over all orthogonal matrices

Let $M=O\Lambda O^\top$ be a positive semi-definite matrix, where $\Lambda\in \mathbb{R}^{p\times p}$ is a diagonal matrix with non-negative entries and $O\in \mathbb{R}^{p\times p}$ is an orthogonal …
John's user avatar
  • 193
0 votes
1 answer
123 views

Define an inner product between p-blades so that 0= completely orthogonal and 1=completely o...

$\DeclareMathOperator\span{span}$Denote two $p$-blades $\nu=v_1\wedge \dots \wedge v_p$ and $\omega=w_1\wedge \dots \wedge w_p$ $\in \bigwedge^p X$, where $X$ is an inner product space. How to define …
John's user avatar
  • 193