9.7 Rank-one Update

#Type/Definition #Topic/Linear_Algebra

Types: N/A
Examples: N/A
Constructions: 9.8 Shear Matrix, 9.9 Dilation Matrix
Generalizations: N/A

Properties: N/A
Sufficiencies: 5.1 Inner Product Between Vectors
Questions: N/A

Rank-one Update

Let matrix $A \in R^{m \times n}$ and vectors $\vec{x} \in R^{m}$ and $\vec{y} \in R^{n}$ . Then, a rank-one update of $A$ is given by

A_{m \times n} + {\vec{x}}_{m \times 1} \cdot {\vec{y}}_{1 \times n}^{T}

Remark. Doing rank one modifications of matrices will be important when we start solving 2B The General Linear-Systems Problem, 3 The Full-Rank Least-Squares Problem, and 4 The Standard Eigenvalue Problem.
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