Let's say I want to perform the conventional matrix multiplication, so I define it as "multiply then sum the products" (i.e. "x,+")
For example, for matrices A and B:
if A = |a b|
.........|c d|
and B = |1 2|
.............|3 4|
Then:
A "x,+" B = | [ax1+bx3] [ax2+bx4] |
.................| [cx1+dx3] [cx2+dx4] |
But if I want to make only sums, I could define the operations as "+,+" (i.e. "sum, and then, sum the sums")
So that:
A "+,+" B = | [a+1+b+3] [a+2+b+4] |
.................| [c+1+d+3] [c+2+d+4] |
Or whatever I want: "(/)^2,-" (i.e. "divide and square the quotient, then substract the squared quotients")
So that:
A "(/)^2,-" B = | [(a/1)^2-(b/3)^2] [(a/2)^2+(b/4)^2] |
.....................| [(c/1)^2-(d/3)^2] [(c/2)^2+(d/4)^2] |
The reason I wanted to do this is because I wanted to make an euclidian distance matrix between some geographic locations (with x,y coordinates)...so I thought the following matrix operation would solve it easily:
A = |x1 y1|
......|x2 y2|
.......|x3 y3|
A' = |x1 x2 x3|
.......|y1 y2 y3|
then the distance matrix is:
sqrt(A "(-)^2,+" A')
where
"(-)^2,+" means "get the difference and square it, then sum the squares"...
and at the end get the square root of each cell... which is Pithagoras' theorem to obtain euclidian distances...
Is there any software which allows defining matrix operations in this way?
This should be possible to calculate in Excel or some other spreadsheet.
However, I don't quite understand your data format. You have a list of locations (2 numbers per location) and you need to create a matrix of euclidean distances for each pair of locations, right?
Dear Przemysław Kowalik,
Yes I have two geographic coordinates per location and I need to obtain the distances for each pair.
Matrix A is comprised by the two coordinate vectors, and matrix A' is the transpose of matrix A, I just wanted to define some unconventional matrix operation, instead of "multiply then sum"; do something like: "get the difference, square it, then sum the squared differences".
It's like I supposed.
So, please find attached a simple example in Excel (5 locations). There are two variants of calculations in the file:
1) Formulas are created with references to entries of the transpose of the initial matrix A.
2) Formulas (slightly more complicated) are created without explicit usage of the transposed matrix, just by using INDEX function and some auxiliary numbers 1,2,3,4,5 placed in a "horizontal" range.
The file is created in Excel 2010, should be compatible with Excel 2007 and newer (also with free LibreOffice Calc, however I haven't tested).
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