What Is the Falk Scheme for Matrix Multiplication?

[transgalactic]

how to multiply two matrices??

i can't understand the rule.

where can i find a good manual to explain
how to multiply two matrices?

 

[FunkyDwarf]

http://en.wikipedia.org/wiki/Matrix_multiplication
http://mathworld.wolfram.com/MatrixMultiplication.html
http://people.hofstra.edu/Stefan_Waner/realWorld/tutorialsf1/frames3_2.html

First three results from a Google search.

 

[HallsofIvy]

Do you know how to take the dot product of two vectors?

If so, think of each row of the "left" matrix and each column of the "right" matrix as a vector. The number in the "i^th row, j^th column" is the dot product of the i^th row of the "left" matrix and j^th column of the "right" matrix.

 

[transgalactic]

i know dot product from physics when
in rigid bodies i was needed to calculate torqe

i did |a|*|b|*cos(angle between them)

can u give me an example of row and column and how to calculate their dot product?

 

[robphy]

$$\vec F\cdot \vec s = \vec F^\top \vec s= \left[ \begin{array}{lll} F_x & F_y & F_z\ \end{array} \right] \left[ \begin{array}{l} s_x & s_y & s_z \end{array} \right]$$
..your turn to do work.

 

[Antineutron]

I think a demonstration of two square matrices would be more helpful for him. I think he needs a demonstation of a multiplication of a 2x2 matrix, and I'm sure he will have no problems afterwards. Sometimes a good demonstration is needed if the student does not have any experience in matrix multiplication. Sometimes we have to assume that student has no background working out matrix multiplication operations.

 

[matt grime]

What do you mean by 'understand'? Can you follow the 'rule', which is just plugging things into an formula?

 

[transgalactic]

i understood that in order to find a certain object in a matrix
we need to do a dot product of a row of one matrix
and a column of another matrix

can some one give me an example
of how to make this dot product in numbers
with a solution

for example how i make a dot product of column
2
3
4

and row 5 6 7
??

 

[HallsofIvy]

i know dot product from physics when
in rigid bodies i was needed to calculate torqe

i did |a|*|b|*cos(angle between them)

can u give me an example of row and column and how to calculate their dot product?

Then I really do feel sorry for you! That's a remarkably difficult definition to use! You will want to learn and use: the dot product of two vectors given in components is
<a b c>.<d e f>= ad+ be+ cf. And it really doesn't matter that they are "row" and "column".

 

[robphy]

i know dot product from physics when
in rigid bodies i was needed to calculate torqe

i did |a|*|b|*cos(angle between them)

Actually torque uses the sin(angle between them).
Since you mentioned dot-product and physics, I thought you would have encountered "work"... which is why I gave my example above in that form.

 

[transgalactic]

thank u all

 

[Edgardo]

Hello transgalactic,

an easy way to multiply matrices is to use the so-called Falk scheme.

1) Here is a video of somebody showing how to use the Falk scheme. It's in German but the calculations
should be self-explanatory.

2) http://statmath.wu-wien.ac.at/courses/glm/matmult.html is another example. In the example you see the Falk scheme on the right side.
Do you see the 8? You get the 8 by "tilting" the column vector (2,1,1) to the row vector (3,2,0) and forming the dot product.

So in your imagination you have the vector (2,1,1) lying on (3,2,0):
(2,1,1)
(3,2,0)
from which you get: 2*3 + 1*2+1*0 = 8

Do you see the 4 (right to the 8)? You get the 4 by "tilting" the column vector (0,2,3) to the row vector (3,2,0) and forming the dot product.

So in your imagination you have the vector (0,2,3) lying on (3,2,0):
(0,2,3)
(3,2,0)
from which you get: 0*3 + 2*2 + 3*0 = 4