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Probability density function and eulers constant

  1. Apr 10, 2012 #1
    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 ?

    Thanks in advance
    Regards
    Mike
     
  2. jcsd
  3. Apr 10, 2012 #2

    micromass

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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.
     
  4. Apr 10, 2012 #3

    micromass

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  5. Apr 10, 2012 #4
    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
  6. Apr 10, 2012 #5

    micromass

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    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)
     
  7. Apr 10, 2012 #6
    am i using the right convention ?

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

    BTW i do mean transpose ...sorry!
     
  8. Apr 10, 2012 #7

    mathman

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    As I stated in the other forum I interpret ABC to mean A.(BC).
     
  9. Apr 10, 2012 #8
    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 ?
     
  10. Apr 10, 2012 #9

    micromass

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    No. A 1x5 times a 5x5 times a 5x1 will yield a 1x1 matrix.
     
  11. Apr 12, 2012 #10

    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
  12. Apr 12, 2012 #11

    micromass

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    Yes, that is correct.
     
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