Property of Matrix Multiplication

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SUMMARY

The discussion confirms the validity of the matrix equation A²·Bᵀ - aA = A(A·Bᵀ - aI), where A and B are matrices and a is a scalar. Participants agree that this transformation is correct due to the distributive property of matrix multiplication over addition. The equation illustrates how scalar multiplication and matrix operations can be manipulated while maintaining equality. This understanding is crucial for anyone working with linear algebra and matrix operations.

PREREQUISITES
  • Understanding of matrix operations, including multiplication and addition
  • Familiarity with scalar multiplication in linear algebra
  • Knowledge of matrix transposition, denoted as Bᵀ
  • Concept of the identity matrix, represented as I
NEXT STEPS
  • Study the distributive property of matrix multiplication in detail
  • Explore scalar multiplication and its effects on matrix equations
  • Learn about the properties of the identity matrix in linear algebra
  • Investigate advanced matrix operations and their applications in various fields
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on linear algebra, matrix theory, and related computational fields.

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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