Probability density function and eulers constant

[mikedamike]

Hi,

I have a probability density function defined by

1 / D x E . e^ABC/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 e^ABC/2 (which is effectivly a 5x1 matrix / 2)?

Can anyone help me with this ?

Thanks in advance
Regards
Mike

 

[micromass]

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.

 

[micromass]

Also, see this http://en.wikipedia.org/wiki/Matrix_exponential

 

[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)

 

[micromass]

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)

 

[mikedamike]

am i using the right convention ?

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

BTW i do mean transpose ...sorry!

 

[mathman]

As I stated in the other forum I interpret ABC to mean A.(BC).

 

[mikedamike]

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 ?

 

[micromass]

No. A 1x5 times a 5x5 times a 5x1 will yield a 1x1 matrix.

 

[sankalpmittal]

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.

 

[micromass]

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.