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Tagged with rank-1-matrices projection-matrices
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$\lambda_{\min}$ and $\lambda_{\max}$ of rank-1 sum of matrices
It is explained from previous posts1,2 that for a rank-$1$ matrix $x_ix_i^T$ we have $\lambda_{\max} (x_ix_i^T)=1$ and $\lambda_{\min} (x_ix_i^T)=0$ with single and $N-1$ algebraic multiplicity, ...
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4
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Rank one orthogonal projector matrix.
My text is covering projector matrices while building up to Householder triangularization. The main topic of discussion is orthogonal projector matrices that satisfy
\begin{align} P &= P^2 \...
- 4,360
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Finding eigenvectors of a rank one projection matrix
From the unit vector $$u=\left(\frac{1}{6},\frac{1}{6},\frac{3}6,\frac{5}6\right)$$ construct the rank one projection matrix
$$P=uu^t.$$
a) Show that if $P=uu^t$ , then $u$ is an eigenvector with $\...
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