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Hey guys, any hints on how to show that [tex]\frac{d}{dt}[/tex]_{|t=0} [tex]det(I + tA) = tr(A) [/tex]? I did it for 2x2 but I can't figure out a generalization. Thanks
radou said:Did you try to use the definition of the determinant to conclude something?
The trace of a matrix is the sum of its diagonal elements. Derivatives, on the other hand, are the rates of change of a function with respect to its variables.
The derivative of a function can be interpreted as the slope of its tangent line at a given point, which is equivalent to the trace of the Jacobian matrix at that point.
Trace and derivatives are used in a variety of fields such as physics, engineering, and economics for optimization, differential equations, and analyzing complex systems.
Yes, trace and derivatives are used in machine learning algorithms for tasks such as gradient descent and backpropagation in neural networks.
Trace and derivatives may not be applicable to non-differentiable functions or in cases where the function is discontinuous or undefined at certain points.