Probability density function and eulers constant

1. Apr 10, 2012

mikedamike

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 Im 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 any one help me with this ?

Regards
Mike

2. Apr 10, 2012

micromass

Staff Emeritus
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.

3. Apr 10, 2012

micromass

Staff Emeritus
4. Apr 10, 2012

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)

Last edited: Apr 10, 2012
5. Apr 10, 2012

micromass

Staff Emeritus
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)

6. Apr 10, 2012

mikedamike

am i using the right convention ?

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

BTW i do mean transpose ...sorry!

7. Apr 10, 2012

mathman

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

8. Apr 10, 2012

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 ?

9. Apr 10, 2012

micromass

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

10. Apr 12, 2012

sankalpmittal

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 ?

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: Apr 12, 2012
11. Apr 12, 2012

micromass

Staff Emeritus
Yes, that is correct.