matrix multiplication

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- anonymous

matrix multiplication

- schrodinger

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- anonymous

comp being slow, pls wait..

- anonymous

ok what is the matrix problem

- anonymous

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

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- anonymous

and what are the dimensions of those matrices

- anonymous

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

- anonymous

and Y another arbitrary angle..

- anonymous

4x4 matrix

- anonymous

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

- anonymous

ok

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

or calculator

- anonymous

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

- anonymous

so u just want to multiply those two matrices

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

do u want AxBxC

- anonymous

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

- anonymous

ok

- anonymous

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

- anonymous

ok thx

- anonymous

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

- anonymous

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

- anonymous

that's fine, i will check later

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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;

- anonymous

the result for linear algebraic multiplication for example
A x B

- anonymous

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

- anonymous

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

- anonymous

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]

- anonymous

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

- anonymous

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]

- anonymous

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.

- anonymous

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

- anonymous

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

- anonymous

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!

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