A geometric note on subspace updates and orthogonal matrix decompositions under rank-one modifications

Ralf Zimmermann

In this work, we consider rank-one adaptations $X_{new}=X+a{b}^T$ of a given matrix $X\in {\mathbb{R}}^{n\times p}$ with known matrix factorization $X=UW$, where $U\in\mathbb{R}^{n…