Is the Matrix B Positive or Not?

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Discussion Overview

The discussion revolves around the classification of a specific matrix B in terms of its positivity, particularly whether it qualifies as a positive matrix or not. The conversation touches on definitions from different sources, including a website and Wikipedia, and explores the implications of these definitions in the context of matrix theory.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant cites a source claiming that matrix B is not positive, while another references Wikipedia, which defines a positive matrix as one with all elements greater than zero.
  • Another participant clarifies that zero is not greater than zero, suggesting that any matrix containing a zero cannot be considered positive.
  • A further distinction is made between nonnegative matrices (elements equal to or greater than zero) and positive matrices (elements strictly greater than zero), indicating that the two terms are not interchangeable.
  • A later reply expresses an acknowledgment of confusion and suggests a need for more rest, implying a recognition of the complexity of the topic.

Areas of Agreement / Disagreement

Participants express differing interpretations of the definitions of positive and nonnegative matrices, indicating a lack of consensus on the classification of matrix B.

Contextual Notes

The discussion highlights potential ambiguities in the definitions of positive and nonnegative matrices, as well as the implications of including zero in a matrix when determining its classification.

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I haven't read the links, but zero is not greater than zero. So why would a matrix containing a zero be "positive"?
 
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From the wiki page,
A nonnegative matrix is a matrix in which all the elements are equal to or greater than zero.
A positive matrix is a matrix in which all the elements are greater than zero.
Nonnegative isn't the same thing as positive.
 
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:oops: Oops. Thanks, Stephen Tashi and Mark44. I should get more sleep...
 

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