Property of Matrix Multiplication

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Discussion Overview

The discussion revolves around the properties of matrix multiplication, specifically examining the validity of a particular algebraic manipulation involving matrices A and B, and a scalar a. The focus is on the distributive property of matrix multiplication over addition.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant presents an algebraic expression involving matrices and asks if the manipulation is correct.
  • Another participant expresses agreement with the proposed manipulation.
  • A third participant confirms the correctness of the manipulation, citing the distributive property of matrix multiplication as the basis for their agreement.

Areas of Agreement / Disagreement

There appears to be agreement among participants regarding the correctness of the manipulation, although the initial query remains open to further discussion.

Contextual Notes

The discussion does not explore potential limitations or assumptions related to the matrices involved or the specific conditions under which the distributive property applies.

Yankel
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Hello, I wanted to ask if this is a correct move, A and B are matrices, a is a scalar, thank you !

A^{2}\cdot B^{t}-aA=A(A\cdot B^{t}-aI)
 
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Yankel said:
Hello, I wanted to ask if this is a correct move, A and B are matrices, a is a scalar, thank you !

A^{2}\cdot B^{t}-aA=A(A\cdot B^{t}-aI)
Seems correct to me.
 
Yankel said:
Hello, I wanted to ask if this is a correct move, A and B are matrices, a is a scalar, thank you !

A^{2}\cdot B^{t}-aA=A(A\cdot B^{t}-aI)

Hi Yankel, :)

Yes, its correct because matrix multiplication is distributive over matrix addition.

Kind Regards,
Sudharaka.
 
Thank you !
 

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