Multiplying a vector with Square Matrix vs. its transpose

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SUMMARY

The discussion focuses on the mathematical operations involving a square matrix A of size n x n and a vector B of size n x 1. It clarifies that multiplying the matrix A by the vector B (A x B) yields different results compared to multiplying the transpose of the matrix A (A') by the vector B (A' x B), unless A is symmetric. In the case of a symmetric matrix, both operations produce the same result. The conversation emphasizes the importance of notation, where capital letters denote matrices and lowercase letters denote vectors.

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  • Understanding of matrix multiplication
  • Knowledge of matrix transposition
  • Familiarity with symmetric matrices
  • Basic linear algebra concepts
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  • Learn about matrix multiplication rules
  • Investigate the implications of matrix transposition
  • Practice with examples of matrix-vector multiplication
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newphysist
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Hi,

I am new to Math so I am trying to get some intuition.

Let's say I have a matrix A of n x n and a vector B of n x 1 what is the difference between A x B and A' x B?

Thanks
 
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I am not sure what you are looking for. I suggest you create some simple examples (n = 2 or 3) and see what you get.
 
newphysist said:
Hi,

I am new to Math so I am trying to get some intuition.

Let's say I have a matrix A of n x n and a vector B of n x 1 what is the difference between A x B and A' x B?
If the matrix A is symmetric, there's no difference between Ab and ATb.

Note that I changed your notation a bit. Capital letters are usually used to represent matrices, and lower case letters are usually used for vectors.
 

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