Homepage › Solution manuals › Gilbert Strang › Linear Algebra and Learning from Data › Exercise 1.9.8

Exercise 1.9.8

Answers

The rank-3 matrix $A = σ_{1} u_{1} v_{1}^{T} + σ_{2} u_{2} v_{2}^{T} + σ_{3} u_{3} v_{3}^{T}$ , so $A - A_{1} = σ_{2} u_{2} v_{2}^{T} + σ_{3} u_{3} v_{3}^{T}$ and $A - A_{2} = σ_{3} u_{3} v_{3}^{T}$ . The $l^{2}$ norm of matrices is the largest singular value of the matrix. So $| | A - A_{1} | |_{2} = σ_{2}$ and $| | A - A_{2} | |_{2} = σ_{3}$ . So $A$ has the same singular values $σ_{2} = σ_{3}$ .

niuers

2020-03-20 00:00

Exercise 1.9.8

Answers

Comments

Add answer