I have read about Directional derivatives and know that to maximize the dot product of gradient vector and u(vector) we have to make cosine 0 deg as its 1. But after we do this we are only left with the magnitude of the gradient and then how we know the direction of the gradient. The gradient vector is partial derivatives of all the dimensions of multivariate functions.
To minimize the cost function in machine learning we need to compute gradient decent algorithm which is :
Weight(new) = weight(old) - alpha * (partial derivatives of all features(gradient vector))
How giving minus sign takes care of all the directions in multidimensional space. Gradient vector in theory must contain direction as its vector but in practical its a number with a sign where is the direction? Can a number with a sign represent all movementsenter image description here?
I don't know where to post this question as computer engineers dont know enough maths that's why I posted it here.
Why the gradient vector gives the direction of maximum increase of a function?
Please refer to this question if my explanation is not clear as its my 1st time posting a query here.