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 Oct 28 comment Speeding Up and Slowing Down of Particle The speed is the absolute value of the velocity. Speeding up means the speed is increasing, which means the acceleration and the velocity have the same sign. Slowing down means the speed is decreasing which means the acceleration and velocity have opposite signs. Oct 12 answered Is this Fourier Transform relation correct? Oct 12 comment Are relative uncertainties additive? @Ian, your formula is based on the uncertainty being defined as the standard deviation. The formula used by the OP is simpler and is based on the uncertainty being defined in terms of derivatives. For instance if $m=ab$ then $\mathrm{d}m/m = \mathrm{d}a/a + \mathrm{d}b/b$. This second formula is sometimes taught in lab classes, thought the use of the standard deviation is more "standard". Oct 12 answered What is the cross product in spherical coordinates? Oct 12 answered A function that is zero for every integer multiple of $k$ Oct 12 comment Non-singularity of a matrix @SahibaArora, Thats the key idea. Problem is your answer assumes $A$ itself is diagonalizable, but this might not be true. It is true that $A^*A$ must have positive eigenvalues, think about how the adjoint works in the inner product and look at the hint by A.G. above. Oct 11 comment Non-singularity of a matrix I'm assuming that the matrix $I+A^*A$ has an eigenvalue of $0$. This leads to the conclusion that $A^*A$ has an eigenvalue of $-1$. The goal is to show that this is not possible for such a matrix and arrive at a contradiction. Oct 11 comment How to complete this partial differential equation? @trapper, should be fixed now. I also had dropped a factor of $\dot{\theta}$ on the very last term. Sorry about that. Oct 11 revised How to complete this partial differential equation? added 43 characters in body Oct 11 comment How to complete this partial differential equation? @trapper, It should have been, I made a mistake. I'll fix it now. Oct 10 comment Why not generalize the Intermediate Value Theorem It would also make the theorem harder to apply. Determining the max/min of a function is more difficult than just evaluating it at the end points. Oct 10 answered Non-singularity of a matrix Oct 10 comment How to Integrate the Differential Equation for the Pendulum Problem @user32882, yes that's right. Oct 10 answered How to Integrate the Differential Equation for the Pendulum Problem Oct 10 comment subtract two 4-digit numbers and obtain the sum of the digits always 18 $1112 - 1111 = 1$ which seems to be a counterexample for your problem. Am I missing something here? Oct 10 answered How to complete this partial differential equation? Oct 10 comment What is the relation between Fourier's Inversion theorem and the Dirac-Delta function? My answer here might be helpful, math.stackexchange.com/questions/991263/… Oct 10 comment Sine representation of cosine See the method I applied in my answer here : math.stackexchange.com/questions/986835/… Oct 10 answered Why is the Fourier transform self-inverse? Oct 9 comment By substituting $z = h(t)$ show that $\delta(h(t))=\sum\limits_{i}\frac{\delta(t−t_i)}{\mid h^{\prime}(t_i)\mid}$ Thank you. You are correct, my $r_i$' are your $t_i$'s. It doesn't really matter how you label them so long as you remember what they represent, i.e., the roots of the function $h$. I called them $r_i$ just to make it easier to distinguish the two when I was writing. If you want to change all the $r$'s to $t$'s you are welcome to edit the answer accordingly.