Message Boards Message Boards

[✓] Write a matrix multiplication with indefinite limits?

GROUPS:

Hello, I need to find an answer to this problem. Let G(t) be a nxn matrix. I need to calculate G(t-1)xG(t-2)x...xG(2)xG(1) where x is the usual matrix multiplication. I can't use the function Product[G(i),{i,t-1,1}] because it uses the usual multiplication of real numbers. Any Idea of how can I solve this?

Answer
3 months ago

The matrix multiplication is Dot in Mathematica. If you need your product for display only, you can inactivate it:

Inactive[Dot][g[t - 1], g[t - 2], \[Ellipsis], g[2], g[1]]

If you need it for actual calculation you can use the infix form of Dot:

g[5].g[4].g[3].g[2].g[1]

or generate the terms with Table:

Dot @@ Table[g[k], {k, 5, 1, -1}]
POSTED BY: Gianluca Gorni
Answer
3 months ago

I'm sorry, I guess I've not been clear. I need to calculate (not only for display) G(t-1)xG(t-2)x...xG(2)xG(1) without setting any value to t. For instance, the product x(x-1)...*(x-t) is equal to Gamma(x+1)/Gamma(x-t). I want to find a closed expression that would depend on t.

Answer
3 months ago

Hmmm. What do you mean by "closed expression"?

Smile, make one of your own. Say your procuct is called U[t] and according to Gianlucas proposal you can write

U[t_?NumericQ] := Dot @@ Table[g[j], {j, 1, t - 1}]

You can use it everywhere:

In[7]:= U[t]

Out[7]= U[t]

Whenever you need it mor explicit give it a t ( element of Integers)

In[6]:= U[4]

Out[6]= g[1].g[2].g[3]
POSTED BY: Hans Dolhaine
Answer
3 months ago

Let me try to explain with an example:

In[249]:= Product[x - i, {i, 0, t - 1}]

Out[249]= (1 - t + x) Pochhammer[2 - t + x, -1 + t]

what I need is the expression in "Out[249]", this is what I mean by "closed expression". Look that the boundary I've used is an unapropriate bound to a Table or to a loop, but it's not to the function "Product". I'm looking for a function that would do the same thing as the function Product but instead of using the usual multiplication of real numbers, it uses the usual matrix product.

Answer
3 months ago

Group Abstract Group Abstract