Matrix Invertability & Singularity: Explained

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Discussion Overview

The discussion revolves around the relationship between matrix invertibility and singularity, specifically whether an invertible matrix can be singular. The scope includes theoretical aspects of linear algebra and definitions related to matrix properties.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions if an invertible matrix can be singular.
  • Another participant asserts that the answer is "no," emphasizing that a non-singular matrix has a non-zero determinant, while a singular matrix has a zero determinant, making it non-invertible.
  • A different participant clarifies that the pseudo-inverse is not the same as the inverse, suggesting a distinction in the context of the discussion.
  • There is an acknowledgment of a previous point made by another participant, indicating a concession in the debate.

Areas of Agreement / Disagreement

Participants generally disagree on the initial question, with some asserting that an invertible matrix cannot be singular, while others provide additional context that may suggest a more nuanced understanding.

Contextual Notes

There are unresolved definitions and assumptions regarding the terms "invertible," "singular," and "pseudo-inverse," which could affect the clarity of the discussion.

phymatter
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if a matrix is invertable can it be singular ?
 
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The link says it calculates the pseudo-inverse. The pseudo-inverse is a well known and useful concept, but it is NOT the same as the inverse.

The answer to the OP's questiion is "no".
 
No, if a matrix is invertible it is said to be non-singular which is the exact opposite of singular.
In other words a singular matrix has got a zero determinant and as such it's inverse cannot be obtained.A non singular matrix has got the determinant not equal to zero and in the due course it's inverse can be obtained hence the name invertible matrix.
 
@AlephZero and kaliro - Point conceeded.

@phymatter please accept my apologies if my post was misleading.
 
thanks for everyone's help :)
 

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