## elica85 2 years ago matrix multiplication

1. elica85

comp being slow, pls wait..

2. mathsmind

ok what is the matrix problem

3. elica85

let x be an arbitrary angle and C represents cosine, S represent Sine

4. mathsmind

and what are the dimensions of those matrices

5. elica85

matrix A= CX -SX 0 aCX SX CX 0 aSX 0 0 1 0 0 0 0 1 matrix B= CY -SY 0 bCY SY CY 0 bSY 0 0 1 0 0 0 0 1

6. elica85

and Y another arbitrary angle..

7. elica85

4x4 matrix

8. elica85

i think i get how to do the multiplication but since there are variables, i'm coming up with crazy figures for each new element in the new matrix. and this new matrix has to be multiplied by another 4x4

9. mathsmind

ok

10. elica85

i guess my problem is more towards trig...is there a simple expressions for each element?

11. mathsmind

i will solve for u as soon as i am done with the other student

12. elica85

thx, or you can just tell me if there's no simple expression cuz i can do all the work, it will just look messy

13. mathsmind

4x4 is a messy matrix, so should expect such a mess

14. elica85

ok. or are you familiar with matlab? from what i remember, you have to have values for matlab...

15. mathsmind

do u want to do this with matlab or using normal mathematical methods

16. elica85

it's just part of the actual problem so i don't think working it out by hand is important so if i can do it on matlab, it would be great

17. elica85

or calculator

18. mathsmind

ok i will do it for u with c++ or c sharp

19. mathsmind

so u just want to multiply those two matrices

20. elica85

i'm not familiar with c++ but there is another matrix, i will type it up..

21. elica85

Matrix C= CZ -SZ 0 cCZ SZ CZ 0 cSZ 0 0 1 0 0 0 0 1

22. elica85

and a,b,c are arbitrary constants. so in c++, you can keep the expression with variables?

23. mathsmind

do u want AxBxC

24. elica85

if that means the same thing as AxB=AB ABxC=result 4x4 matrix

25. mathsmind

ok

26. mathsmind

no it does not mean the same thing but i get what u want now

27. elica85

ok thx

28. mathsmind

am sorry of the delay just someone before u sent me a bunch of questions that i need to type the answers

29. mathsmind

so u can do others stuff and i will finish the work for u as soon as possible

30. elica85

that's fine, i will check later

31. mathsmind

sorry for keeping u waiting but i need to know do u want element by element multiplication or linear algebraic product

32. mathsmind

you have to be precise on that so i can give u the right answer

33. elica85

good question, i was actually trying to figure out on google. all the instructor said was to multiply them. what i found on google was this http://easycalculation.com/matrix/learn-matrix-multiplication.php which is what's going to make the result matrix look real messy. the problem is to find the transformation matrix of a mechanical grabber. so it would have multiple joints, point O as fixed, and point P as the position of the grabber. to find the position, find transformation matrices (which i've done) and the post multipy the matrices to get the result matrix. the matrix C was from point O to joint 1, matrix B is from joint 1 to joint 2, and matrix A is from joint 2 to point P

34. mathsmind

HI THERE I KNOW IT TOOK ME A LONG TIME BUT I PROMISED SOMEONE TO FINISH THERE 50 QUESTIONS

35. mathsmind

syms cosx sinx asinx acosx cosy siny bcosy bsiny cosz sinz csinz ccosz syms cosx sinx asinx acosx cosy siny bcosy bsiny cosz sinz csinz ccosz A=[cosx, -sinx,0, acosx;sinx,cosx,0,asinx;0,0,1,0;0,0,0,1]; B=[cosy, -siny,0, bcosy;siny,cosy,0,bsiny;0,0,1,0;0,0,0,1]; %C=[cosz, -sinz,0, ccosz;sinz,cosz,0,csinz;0,0,1,0;0,0,0,1]; %Linear algebraic product of the matrices... M1= A * B * C; M2= A*B; M3= B*C; M4= A*C; %Array arithmetic operations are carried out element by element M1= A * B * C; M2= A*B; M3= B*C; M4= A*C;

36. mathsmind

the result for linear algebraic multiplication for example A x B

37. mathsmind

A = [ cosx, -sinx, 0, acosx] [ sinx, cosx, 0, asinx] [ 0, 0, 1, 0] [ 0, 0, 0, 1]

38. mathsmind

B = [ cosy, -siny, 0, bcosy] [ siny, cosy, 0, bsiny] [ 0, 0, 1, 0] [ 0, 0, 0, 1]

39. mathsmind

A*B ans = [ cosx*cosy - sinx*siny, - cosx*siny - cosy*sinx, 0, acosx + bcosy*cosx - bsiny*sinx] [ cosx*siny + cosy*sinx, cosx*cosy - sinx*siny, 0, asinx + bsiny*cosx + bcosy*sinx] [ 0, 0, 1, 0] [ 0, 0, 0, 1]

40. mathsmind

so this is what u called messy result which seems to be exclusive of your intuitive expectation, however the element by element matrix multiplication would give a result hopefully to your expectation

41. mathsmind

A.*B ans = [ cosx*cosy, sinx*siny, 0, acosx*bcosy] [ sinx*siny, cosx*cosy, 0, asinx*bsiny] [ 0, 0, 1, 0] [ 0, 0, 0, 1]

42. mathsmind

Array arithmetic operations are carried out element by element, and can be used with multidimensional arrays. The period character (.) distinguishes the array operations from the matrix operations.

43. mathsmind

Sorry i was busy but i have to keep all my promises not matter what, so all the best and good luck.

44. mathsmind

Now with this basic method you can do whatever multiplication you want, and in any associative, distributive ... way you want.

45. elica85

thank you, i think i will have to ask which multiplication is needed since i don't know. i would hope it's the easier one though!