Matrix Algebra

[brian728s]

Can anyone provide me with an algorithm to multiply 2 matrices (If possible it needs to work with vectors too) for vb.net?

[Guv]

Product^row_column = Sum[ A^row_x * B^x_column ] for all values of x.

Where Product is the matrix product of matrices A, B

Note that for matrices, multiplication is not commutative: A*B seldom equals B*A

If you do not grok the above formula, the following is the formula for The element in row 2 column 3 of the product of A and B, assuming A and B are 4X4 matrices.

Product²₃ = A²₁* B¹₃ + A²₂* B²₃ + A²₃* B³ ₃ + A²₄* B⁴₃

Superscripts represent rows and sub scripts represent colums.

Note that rectangular matrices can be multiplied.

If A is a 4X5 (4 rows & 5 columns), while B is a 5X4 (5 rows & 4 columns), the above general formula would work. The product would be a 4X4 matrix. For the element in row 2 column 3, the formula would be the following.

Product²₃ = A²₁* B¹₃ + A²₂* B²₃ + A²₃* B³ ₃ + A²₄* B⁴₃ + A²₅* B⁵₃

The above uses tensor notation. For vectors, ordinary notation is usually used.

Product = A₁* B₁ + A₂* B₂₁ + A₃* B₃

Where Product is the scalar product of two 3D vectors: A & B.

Tensor notation is preferred for matrices because there is an obvious pattern to correct formulae, making it easy to find typo's

[brian728s]

I know that already. Can anyone post vbcode to do it? (I was taught a while ago, and was dependant on a calculator to do it)

[Guv]

Brian728s: Post code for this? How much do you know about VB syntax and programming?

I do not use VB Net, but it cannot be that much different from VB 6.0

How about something like the following?

Dim A(0 To 10, 0 To 10) As Double
Dim B(0 To 10, 0 To 10) As Double
Dim Product(0 To 10, 0 To 10) As Double
 
Dim J As Integer
Dim K As Integer
Dim X As Integer
 
 
For J = 0 To 10
        For K = 0 To 10
                Product(J, K) = A(J, X) * B(X, K)
                For X = 1 To 10
                        Product(J, K) = Product(J, K) + A(J, X) * B(X, K)
                    Next X
            Next K
    Next J

Perhaps you need a good book (try one of Sam's) or a course. The above should be easy once you know the matrix multiply algorithm. I think you need more help than you can find here.