Self note on Linear maps of the following type: Let x in R and let a be constant, and let L be a linear map, then if L(a*x/|x|) < 1, then we have a*L(x/|x|) < 1, and multiplying by |x| on both sides, we have a*|x|*L(x/|x|) < |x|. Given linearity of L, however, we can write a*L(x/|x| +...{|x|times}...+x/|x|)= a*L(|x|*x/|x|) < |x|. Then a*L(x) < |x|. Any issues problems with this (normally one might expect |x| to be an integer in applying linearity here, or in other words when dealing with irrationals should there be any issues applying linearity in this manner?
Sunday, June 22, 2014
Self note on Linear Maps and a bit of algebra
Self note on Linear maps of the following type: Let x in R and let a be constant, and let L be a linear map, then if L(a*x/|x|) < 1, then we have a*L(x/|x|) < 1, and multiplying by |x| on both sides, we have a*|x|*L(x/|x|) < |x|. Given linearity of L, however, we can write a*L(x/|x| +...{|x|times}...+x/|x|)= a*L(|x|*x/|x|) < |x|. Then a*L(x) < |x|. Any issues problems with this (normally one might expect |x| to be an integer in applying linearity here, or in other words when dealing with irrationals should there be any issues applying linearity in this manner?
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from gi.repository import Gtk, Gdk, cairo, Pango, PangoCairo import math import sys RADIUS = 150 N_WORDS = 10 FONT = "Sans Bold 27...
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I've looked through a series of web sites on this topic, any number of these ranging in various degrees of technical information, but... -
from gi.repository import Gtk, GdkPixbuf, Gdk import os, sys import math class GUI: def draw_callback(guiobj, widget, cr): ...
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