Question

Hi there! I'm trying to understand how the (float) power of matrix works. Could you help me with that?

Answer 1

The power of float or the power of matrices?

Answer 2

Float (in computing) is simply a way to specify that you have a considerable number of floating points after a number (or simply decimal points).
This helps provide precision when dealing with sensitive data, but it also makes computation slower.
An example below:

Answer 3

i have a shear matrix M and i'm trying to do: M^x (where x can be a float value)

Answer 4

x being float, complicates the problem because you have to use more rigorous methods.
For example: M^4 is easy because you just multiply the matrix by itself 4 times. For M^3.54235, the power is a float type, so it become complicated.
The power of making such a generalization though is that you can make very interesting results from this.

Answer 5

Just as it it easier to compute x^6 than to compute x^4.33

Answer 6

this is exactly what i'm trying to do... x being an integer isn't sufficient for me

Answer 7

do you know how to compute this (with a shear matrix that has just 1 eigenvector)?

Answer 8

So are you needing a method to generalize to floating point numbers or do you just want to know why it's important?

Answer 9

i need a method

Answer 10

i'm writing a game engine and i need this to do some manipulations to objects in the world

Answer 11

Do you know how to find eigenvalues and vectors?

Answer 12

not exactly
i know what they are, but i don't understand how they work or what they have to do with the power of matrix

Answer 13

Okay, I'll explain to a point, but I need to know how much of matrices you already know.

Answer 14

i know how to multiply them

Answer 15

i see the columns as vectors in space

Answer 16

Do you have a math tool for work or are you seeking to do all this by hand?

Answer 17

maybe we can use an online whiteboard

Answer 18

Yeah, show me one.

Answer 19

http://www.twiddla.com/1493766

Answer 20

i don't know if you're able to edit it as well