Probability density function and eulers constant

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Discussion Overview

The discussion revolves around the formulation and interpretation of a probability density function involving matrix operations and Euler's constant. Participants explore the mathematical validity of matrix multiplications and the implications of matrix dimensions in the context of the function presented.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Mike presents a probability density function involving a matrix determinant and Euler's constant, questioning how to handle the expression involving a 5x1 matrix divided by 2.
  • Some participants challenge the multiplication of matrices, noting that the dimensions must align for valid operations, specifically pointing out issues with multiplying a 5x1 matrix and a 5x5 matrix.
  • Clarifications are made regarding the dimensions of matrices A, B, and C, with some participants asserting that A should be the transpose of C, thus changing its dimensions from 5x1 to 1x5.
  • There is a discussion about the matrix exponential, with participants questioning whether it can be applied to non-square matrices.
  • Some participants assert that the resulting dimensions from the matrix multiplications lead to a 1x1 matrix, while others confirm the correctness of the multiplication rules being discussed.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of certain matrix multiplications and the interpretation of matrix dimensions. There is no consensus on how to resolve the initial question posed by Mike, and the discussion remains unresolved regarding the application of Euler's constant in this context.

Contextual Notes

Limitations include potential misunderstandings of matrix multiplication rules and the implications of using transposes, as well as the conditions under which matrix exponentials can be applied.

mikedamike
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Hi,

I have a probability density function defined by

1 / D x E . eABC/2

D is a single number
E is a determinant of a matrix
. is the dot product between the two sides of the function
e I am pretty sure is meant to be eulers constant
A is a 5x1 vector
B is a 5 x 5 matrix
C is a 5x1 vector

To my understanding eulers constant can only be raised to the power of a single number
My question is that how can the second half of the equation be solved if i require eABC/2 (which is effectivly a 5x1 matrix / 2)?

Can anyone help me with this ?

Thanks in advance
Regards
Mike
 
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Your multiplication ABC makes no sense. If A is a 5x1-matrix and if BC is a 5x1 matrix, then there is no way to multiply those. Unless you're looking at some sort of dot-product.
 
sorry ill make this more clear

A - This is a 5x1 matrix ( where A is actually the transpose of c)

B - this is a 5x5 matrix

c - this is a 5x1 matrix

This would mean axb = ab (5x1 )

ab X c = abc(5x1)
 
Last edited:
You can't multiply a 5x1 matrix and a 5x5 matrix.

Do you mean that A is the transpose of C? That way, A would be a 1x5 matrix! (which would make sense)
 
am i using the right convention ?

using MY description i have used [rows] x [columns]

BTW i do mean transpose ...sorry!
 
As I stated in the other forum I interpret ABC to mean A.(BC).
 
Sorry you are correct

it is

1x5 x 5x5 x 5x1

= 5x1

However this still mens i have a 5x1 /2

Also matrix exponential can only be done on square matrix ?
 
No. A 1x5 times a 5x5 times a 5x1 will yield a 1x1 matrix.
 
  • #10
micromass said:
No. A 1x5 times a 5x5 times a 5x1 will yield a 1x1 matrix.
Side question : 1x5 times 5x5 matrix will be 1x5 matrix right ? Then 1x5 times 5x1 matrix can yield 1x1 because for a matrix to multiply , columns of first matrix must be equal to rows of second matrix , i.e. r2=c1.

Am I correct ?

@Mikedamike
sorry ill make this more clear

A - This is a 5x1 matrix ( where A is actually the transpose of c)

B - this is a 5x5 matrix

c - this is a 5x1 matrix

This would mean axb = ab (5x1 )

ab X c = abc(5x1)
ab will be 1x5 matrix and not 5x1. You cannot multiply 5x1 times 5x1 because for two matrices to multiply , rows of second matrix must be equal to columns of first matrix but 1 is not equal to 5.
 
Last edited:
  • #11
sankalpmittal said:
Side question : 1x5 times 5x5 matrix will be 1x5 matrix right ? Then 1x5 times 5x1 matrix can yield 1x1 because for a matrix to multiply , columns of first matrix must be equal to rows of second matrix , i.e. r2=c1.

Am I correct ?

Yes, that is correct.
 

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