- #1

mikeph

- 1,235

- 18

http://www.mathworks.co.uk/products/matlab/demos.html?file=/products/demos/shipping/matlab/inverter.html

[PLAIN]http://www.mathworks.co.uk/products/demos/shipping/matlab/inverter_01_thumbnail.png

^^^ Random matrix, 100x100

[PLAIN]http://www.mathworks.co.uk/products/demos/shipping/matlab/inverter_02_thumbnail.png

^^^ Inverse of this random matrix.

The given reason is; "each element in this matrix ("b") depends on every one of the ten thousand elements in the previous matrix ("a")." but that still makes it random... right?

So... if each element is dependant on 10,000 other elements, it must be pretty random as well. My knowledge on linear algebra is pretty weak, but I'm pretty sure this inverse matrix is unique, so isn't there some sort of loss of information entropy going on here if we go from a very random looking picture to a very un-random looking picture through a one-to-one function?

What's going on?

[PLAIN]http://www.mathworks.co.uk/products/demos/shipping/matlab/inverter_01_thumbnail.png

^^^ Random matrix, 100x100

[PLAIN]http://www.mathworks.co.uk/products/demos/shipping/matlab/inverter_02_thumbnail.png

^^^ Inverse of this random matrix.

The given reason is; "each element in this matrix ("b") depends on every one of the ten thousand elements in the previous matrix ("a")." but that still makes it random... right?

So... if each element is dependant on 10,000 other elements, it must be pretty random as well. My knowledge on linear algebra is pretty weak, but I'm pretty sure this inverse matrix is unique, so isn't there some sort of loss of information entropy going on here if we go from a very random looking picture to a very un-random looking picture through a one-to-one function?

What's going on?

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