Matrixes seem to have a lot of wonderful properties, for example they may help checking if given triangles represented each by three complex numbers (verticles) are simillar.
So, two triangles represented by complex numbers 
![\det{\left[\begin{array}{ccc} \omega_1 & \omega_2 & \omega_3 \\ z_1 & z_2 & z_3 \\ 1 & 1 & 1 \\ \end{array}\right]} = 0](http://s3.wordpress.com/latex.php?latex=%5Cdet%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D+%5Comega_1+%26+%5Comega_2+%26+%5Comega_3+%5C%5C+z_1+%26+z_2+%26+z_3+%5C%5C+1+%26+1+%26+1+%5C%5C+%5Cend%7Barray%7D%5Cright%5D%7D+%3D+0+&bg=ffffff&fg=000000&s=0 "\det{\left[\begin{array}{ccc} \omega_1 & \omega_2 & \omega_3 \\ z_1 & z_2 & z_3 \\ 1 & 1 & 1 \\ \end{array}\right]} = 0")
Proof coming soon.
Filed under: Science, Theory | 2 Comments
Tags: complex, det, determinant, math, numbers, similar, triangles
It’s a test message
the proof is easy i guess.
Similarity of triangles arises from same scale transformation and/or a location transformation on the vertices. And in the matrix, [w1 w2 w3] is dependent on [z1 z2 z3] and [1 1 1] iff this happens. Hence proved !! … isn’t it ?