Hello,I have a question. If A and B are NND matrices, how to prove

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Discussion Overview

The discussion revolves around proving a relationship involving the column spaces of nonnegative definite (NND) matrices A and B. Specifically, the question is whether the column space of A, denoted C(A), belongs to the column space of the sum of A and B, C(A+B). Participants explore definitions and notations related to the topic, as well as approaches to the proof.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks how to prove that C(A) belongs to C(A+B) for NND matrices A and B.
  • Another participant requests clarification on the notation used, specifically what NND and "C" refer to.
  • A participant clarifies that NND stands for nonnegative definite and that C refers to the column space.
  • There is a question about the meaning of C(A, B) and the notation (A,B)transpose[(I,0)].
  • A participant expresses confusion about the original question and seeks tricks or insights into the proof without focusing on the notation issues.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the proof or the notation, and multiple questions and clarifications remain unresolved.

Contextual Notes

There are limitations in the discussion regarding the definitions of terms and the notation used, which may affect the clarity of the proof approach.

xihashiwo
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Hello,

I have a question. If A and B are NND matrices, how to prove C(A) belongs to C(A+B)?

I can prove that C(A)<C(A,B) by using A=(A,B)transpose[(I,0)], and I also can prove C(A+B)<C(A,B) using the similar approach.

But I cannot move further because my thoughs maybe not related to the answer at all.

Can someone help? Many thanks.
 
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You need to explain your notation. What's NND? what's "C" ?
 


NND is nonnegative definite, C is column space
 


Also, I get that C(A + B) is the column space of the matrix sum, A + B, but what does C(A, B) mean? And this - (A,B)transpose[(I,0)].
 


Please no worry about those stuff, I am just confused about my original question, why C(A) belongs to C(A+B), is there any tricks?

Mark44 said:
Also, I get that C(A + B) is the column space of the matrix sum, A + B, but what does C(A, B) mean? And this - (A,B)transpose[(I,0)].
 

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