Originally Posted by JPA Cate
Okay, I'll display my ignorance here: I've heard of vectors. But what on earth is an Eigenvector? (Oh, and just like the radical feminist peeing contest, that one was "no hands", well no maths allowed.)
Yep to what other said, but I'll expand somewhat more so that it will make sense why I named the boat
From a pure mathematical definition a Vector has a magnitude and direction as opposed to a Scalar which only has a magnitude. The vector is defined as X,Y,Z in 3D or we can run in 2D which would be X,Y.
When you multiply 2 vectors together you end up with a resulting vector with a new magnitude and direction. There is a special case in which the direction didn't change but only the magnitude. (The vector became longer or shorter) One of the original vectors in this case is called an Eigenvector because any vector you multiply by it results in just another vector either longer or shorter, but same direction of the Eigenvector.
So now that the math is out of the way……….Math is the foundation for all sciences, the equations are same but the variable just mean different things. For me, as an engineer
this applies to Heat Transfer, Thermo, Fluid Dynamics, and Stress analysis. Same equations just different meaning for the variables.
An example where I routinely utilize Eigenvectors is in determining the Bulking of Structural Members under load. I calculate what the Eigenvector is for the stiffness matrix of the structural system and this results in the way the structure will buckle or collapse (using Finite Element Analysis for this). So when you when you go too deep, your hull
buckles, if you go way too deep it still buckled the same way, regardless of the input pressure as long as it is sufficient.
So if my boat
is an Eigenvector and the Wind
is an arbitrary Vector, and I multiply Wind
x Boat it would continue in the same direction with only the speed changing but not the course via adjusting the sails
<Insert Paul Harvey here>
I guess I could have named it something simple but Math paid for the boat and everything else I have. However that underpowered dinghy
I have IS a Scalar.