Eigenvalue Problem: Directional Loss & Consequences

[jason.bourne]

Many kinds of mathematical objects can be treated as vectors: functions, harmonic modes, quantum states, and frequencies, for example. In these cases, the concept of direction loses its ordinary meaning, and is given an abstract definition. Even so, if this abstract direction is unchanged by a given linear transformation, the prefix "eigen" is used, as in eigenfunction, eigenmode, eigenstate, and eigenfrequency.

source: http://en.wikipedia.org/wiki/Eigenvalue



what are directional losses?
what are its consequences?

 

[Defennder]

You are misreading the quoted text. There is nothing there about "directional losses", which I should say reminds me of an inefficient engine for some reason. The article says though vectors are often associated with direction, they may not always be and if those concepts which may be interpreted mathematically as directions remain untouched by a linear transformation, they are prefixed with "eigen-".

 

[ObsessiveMathsFreak]

"Direction", in the context of eigenvector and eigenvalues, does not always have its original intuative meaning. It's easy for everyone to understand that the vectors (1,2) and (3,4) have different "directions". You can draw a picture. It's less easy to accept that the functions(vectors) cos(x) and sin(x) have different "directions". Essentially we are overloading[/PLAIN] the english word "direction" to represent concepts far beyond its original scope.

 

[jason.bourne]

okay. i got it.

thank you very much guys