Describe the physical interpretation of Jacobian with one example. 50 pts + follow
Answers
heya mate......✌
Answer:
The Jacobian is the matrix that represents the linear transformation that takes a small change in the input of a function to the corresponding small change in output:
The Jacobian is the matrix that represents the linear transformation that takes a small change in the input of a function to the corresponding small change in output:For f:Rn→Rm, a fixed x∈Rn, we have
The Jacobian is the matrix that represents the linear transformation that takes a small change in the input of a function to the corresponding small change in output:For f:Rn→Rm, a fixed x∈Rn, we havef(x+h)=f(x)+J(x)h+o(|h|)for h∈Rm,h→0
The Jacobian is the matrix that represents the linear transformation that takes a small change in the input of a function to the corresponding small change in output:For f:Rn→Rm, a fixed x∈Rn, we havef(x+h)=f(x)+J(x)h+o(|h|)for h∈Rm,h→0provided that the various partial derivatives exist and behave sufficiently nicely.
The Jacobian is the matrix that represents the linear transformation that takes a small change in the input of a function to the corresponding small change in output:For f:Rn→Rm, a fixed x∈Rn, we havef(x+h)=f(x)+J(x)h+o(|h|)for h∈Rm,h→0provided that the various partial derivatives exist and behave sufficiently nicely.In this way the Jacobian is the direct analogue of the derivative in ordinary real analysis.
hope it helps you.....♥
good night ☘
The Jacobian can be thought of as a direction vector in constraint space.
This direction always points towards the target in the direction that requires the least work to be done.
Since this "direction" Jacobian is derived offline, all that needs to be solved for is the magnitude of the force to be applied in order to uphold the constraint.
PS:
This magnitude is called λ ( known as the Lagrange Multiplier.)
long story short, Jacobian is just a consequence of geometric distortion due to transformation
HOPE IT HELPS U MATE