تقرير
The Pseudoinverse of $A=CR$ is $A^+=R^+C^+$ (?)
| العنوان: | The Pseudoinverse of $A=CR$ is $A^+=R^+C^+$ (?) |
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| المؤلفون: | Karpowicz, Michał P., Strang, Gilbert |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 15A09, 15A23, 15A24, 65F45, 65F55, 68W20 |
| الوصف: | This paper gives three formulas for the pseudoinverse of a matrix product $A = CR$. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse $A^+_r$ may be very useful when $A$ is a very large matrix. 1. $A^+ = R^+C^+$ when $A = CR$ and $C$ has independent columns and $R$ has independent rows. 2. $A^+ = (C^+CR)^+(CRR^+)^+$ is always correct. 3. $A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+$ only when $\mathrm{rank}(P^TA) = \mathrm{rank}(AQ) = \mathrm{rank}(A)$ with $A = CR$. Comment: 10 pages, 5 figures, matlab code, new paragraphs introduce general formulas for the pseudoinverse of CR, new Figures and the randomized pseudoinverse algorithm |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2305.01716Test |
| رقم الانضمام: | edsarx.2305.01716 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |