Abstract
Our work is motivated by a theorem proved by von Neumann: Let and be subspaces of a closed Hilbert space and let . Then
where denotes the orthogonal projection of onto the subspace . We look at the linear algebra realization of the von Neumann theorem in . The matrix that represents the composition has a form simple enough that the calculation of becomes easy. However, a more interesting result lies in the analysis of eigenvalues and eigenvectors of and their geometrical interpretation. A characterization of such eigenvalues and eigenvectors is shown for subspaces with dimension .
Citation
Rudy Joly. Marco López. Douglas Mupasiri. Michael Newsome. "Spectral characterization for von Neumann's iterative algorithm in $\mathbb{R}^n$." Involve 6 (2) 243 - 249, 2013. https://doi.org/10.2140/involve.2013.6.243
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