What's the Difference Between x_transpose*x and x*x_transpose?

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Discussion Overview

The discussion centers on the mathematical differences between the expressions x_transpose*x and x*x_transpose, where x is defined as a column vector. Participants explore the implications of these expressions in terms of their resulting forms and properties, touching on concepts of vector norms and matrix multiplication.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant states that x_transpose*x results in the sum of squares of the vector components, equating to the norm of x squared.
  • The same participant questions the nature of x*x_transpose, suggesting it results in an n-by-n matrix.
  • Another participant seeks clarification on the meaning of the asterisk used in the expressions, noting that it can sometimes denote a complex conjugate transpose.
  • A further reply clarifies that the asterisk is used to denote multiplication in this context.
  • One participant explains the general rule of matrix multiplication regarding the dimensions of the resulting matrix when multiplying two matrices.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the notation and implications of the asterisk, and there is no consensus on the interpretation of x*x_transpose beyond the suggestion that it is an n-by-n matrix.

Contextual Notes

There are unresolved assumptions regarding the notation used, particularly the meaning of the asterisk, and the specific definitions of the matrices involved in the discussion.

flufypancakes
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x is a vector - (x1,x2, ..., xn)_transpose (i.e. a column vector). so when we have x_transpose*x we have x1^2+ x2^2+...+xn^2 = norm(x)^2.

right...

now what's x*x_transpose, i.e. column times the row? is it an n-by-n matrix?

actually now that I'm finished typing it I'm pretty sure it is, but i'll still post it to be sure..
 
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What does your asterisk mean? Sometimes an asterisk means the complex conjugate of a transpose, but I'm not sure that's how you mean it here.
 
* means "times" as in 2*2=4
 
The definition of matrix multiplication is that when you compose an i by j matrix with a j by k matrix you get an i by k matrix.
 

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