Matric Proof: A, X', and Inverse - All You Need to Know | AA=A

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Discussion Overview

The discussion revolves around the properties of a matrix defined as A = I - X(X'X)⁻¹X', focusing on whether certain matrices must be square and the idempotent nature of matrix A. The scope includes theoretical aspects of linear algebra and matrix properties.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Post 1 poses several questions regarding the necessity for matrices A, X, and (X'X) to be square, and asks for proof of whether A is idempotent.
  • Post 3 reiterates the need for Yes/No answers to the questions posed in Post 1, emphasizing the identity matrix's role.
  • Post 5 expresses confusion over the notation used in the definition of A, indicating a lack of clarity in the formulation.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there is confusion regarding the initial question and notation, leading to differing levels of understanding and engagement.

Contextual Notes

There are limitations in clarity regarding the notation and definitions used, which may affect participants' ability to engage with the mathematical concepts being discussed.

BigDave48
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Let A= I - X(X'X)inverseX' to clarify: '=transpose; inverse of quantity (X'X)

1. Must A be a square matrix?
2. Must (X'X) be a square matrix?
3. Must X be a square matrix?
4. Show whether matrix A is an idempotent matrix (i.e. that AA=A)

Thanks.
 
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im so stupid! i can't follow aNY OF THAT. if i could understand the question i could answer it instantly.
 
Sorry. I really would appreciate some help.

To be more clear: I is an identity matrix

Questions 1,2,and 3 are essentially Yes/No with a provided proof or explanation.

Does this help, clarify?

Thanks.
 
come on man.
 
What do you mean by
"Let A= I - X(X'X)inverseX' to clarify: '=transpose; inverse of quantity (X'X)"

Sorry but it's incomprehensible.
 

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