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1d
accepted The determinant of the transposing endomorphism
1d
comment The determinant of the transposing endomorphism
ah I see now what you mean thank you!!
1d
comment The determinant of the transposing endomorphism
basically you are saying that if $E=E_1\oplus E_2$ and $f$ is an endomorphism of $E$ such that we can write $f$ as $f=f_1\oplus f_2$ then $det(f)=det(f_1).det(f_2)$ ? is this what you are saying ? if yes where can i find something to read on this. Thanks !
1d
comment The determinant of the transposing endomorphism
Any matrix $M$ is written uniquely as $M=A+S$ so $f(M)=f(A)+f(S)=-A+S=id(A)+id(S)$. After that i don't see how do you get to the product of the determinants especially that the function $det$ is not linear !! I know that this is true for composition of endomorphisms : $det(v\circ u)=det(v).det(u)$ but here i don't see what you did.
1d
asked The determinant of the transposing endomorphism
Apr
26
awarded  Popular Question
Apr
22
awarded  Popular Question
Apr
7
awarded  Popular Question
Mar
30
accepted two equivalents equations with different representations in the plane
Mar
30
comment two equivalents equations with different representations in the plane
Yes I see that, but can we say that the cartesian equation represents the graph only for $x>0$ or can we say that the parametric equations above is a parametrization of only the first part in the first quadrant of the equation.. that is $ \begin{cases} x = 4e^{t/4} \\ y = 3e^{t} \\ \end{cases} $ if and only if $y=\frac{3x^4}{256}$ and $x>0$ so without the part $x>0$ the parametrization is false, Am I right ?
Mar
30
asked two equivalents equations with different representations in the plane
Mar
29
accepted Points of intersection of two parametric curves
Mar
29
asked Points of intersection of two parametric curves
Mar
14
comment area between polar equation $r = \sin\theta$ and $r = \cos\theta$
yes the area is $\frac{\pi}{8}-\frac{1}{4}$
Mar
11
comment Equivalent matrices represent the same linear map in different bases
Thank you, that was the answer i'm looking for!
Mar
11
accepted Equivalent matrices represent the same linear map in different bases
Mar
11
comment Equivalent matrices represent the same linear map in different bases
Could you please elaborate, I don't see what you are saying. Thanks!
Mar
11
comment Equivalent matrices represent the same linear map in different bases
I'm talking about equivalent matrices not similar matrices. $A$ and $B$ are not square matrix they are of type $(n,p)$.
Mar
11
asked Equivalent matrices represent the same linear map in different bases
Mar
7
accepted Evaluating the integral $S=\int_0^12\pi t^4\sqrt{9t^2+4}dt$