MuPAD unable to get the expected representation

Hi,

When I open MuPAD Notebook and type the following commands:

Ac := matrix([[0,1,0], [0,0,1], [0,0,0]]):
Dc := matrix([0,0,1]):
expre1 := exp((tk-tau)*Ac)*Dc:
expre2 := expre1*q*expre1':
Q := int(expre2, tau = tk-T..tk):
Simplify(Q)

to calculate the matrix Q, the result returned is an integral representation.

How to get the following expected results by using MuPAD,

Q(1,1) = (T^5*q)/20

Q(1,2) = (T^4*q)/8

Q(1,3) = (T^3*q)/6

Q(2,1) = (T^4*q)/8

Q(2,2) = (T^3*q)/3

Q(2,3) = (T^2*q)/2

Q(3,1) = (T^3*q)/6

Q(3,2) = (T^2*q)/2

Q(3,3) = T*q

Thanks in advance.

[Walter Roberson]

Ac is going to be 3 x 3.

Dc is going to be 1 x 3.

For the exp((tk-tau)*Ac) part, are you intending matrix exponentiation or element-by-element exponentiation?

Either way, I think the result will be 3x3 -- and that cannot be right-multiplied by 1 x 3

[Zhu]

Thanks for reply. As you say, Ac is a 3-by-3 matrix

In MuPAD, Dc := matrix([0,0,1]) is equivalent to Dc := matrix(3,1,[0,0,1]), so Dc is a 3-by-1 column vector

and exp((tk-tau)*Ac) is the matrix exponential of (tk-tau)*Ac

I check the code again. It seems the syntax is valid, but can't get the result as expected

Answer 1

[Walter Roberson]

In MuPAD, exp() is not the matrix exponential; see http://www.mathworks.com/help/symbolic/mupad_ref/exp.html and http://www.mathworks.com/help/symbolic/mupad_ref/numeric-expmatrix.html