M
  • M
why is direction of gradient vector steepest?
Mathematics
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M
  • M
why is direction of gradient vector steepest?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
....erm..can you make your question a bit clearer?
M
  • M
steepest derivative, it says walk in the direction of gradient vector
anonymous
  • anonymous
whats the equation given

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M
  • M
just the general directional vector |U||del(f)}cos(theta)
M
  • M
Duf
M
  • M
gradient represents the steepest rate of increase of some function for each of the points where the function is defined, but each gradient vector is also perpendicular to the level tangent directions at a point. Note that these gradient vectors are not "normal" to the surface of the hill - as in pointing up into the sky. They are normal to level directions.
anonymous
  • anonymous
The dell is always unitized, that means it is always positive, it is related to the slope, derivative, positve slope.
M
  • M
why is gradient vector the steepest ascent?
anonymous
  • anonymous
It has a relation to the cos function which is merely between 1 and -1. It always end on the +1 side.
M
  • M
and max is when cos = 1?
anonymous
  • anonymous
Yeah, in fact the magnitude of unit vector is equal to 1 so it always win out.
M
  • M
thanks

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