Step-by-step explanation:
(b) If
then
Note that
cancel out so we get

Solving for
we get

(c) I'm not sure what the problem is asking for but here goes. As r doubles,
becomes

The purpose of the tensor-on-tensor regression, which we examine, is to relate tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without being aware of its intrinsic rank beforehand.
By examining the impact of rank over-parameterization, we suggest the Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) methods to address the problem of unknown rank. By demonstrating that RGD and RGN, respectively, converge linearly and quadratically to a statistically optimal estimate in both rank correctly-parameterized and over-parameterized scenarios, we offer the first convergence guarantee for the generic tensor-on-tensor regression. According to our theory, Riemannian optimization techniques automatically adjust to over-parameterization without requiring implementation changes.
Learn more about tensor-on-tensor here
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F-1(x)=x/4 represents the inverse function because to find the inverse you have to interchange the variables & solve for y
Answer:
103
Step-by-step explanation:
So the .4 in the tenths place is less than 5 it is rounded down/stays the same so its 103
Hope this helps!!
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