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Feb
13
comment What does it mean to represent a number in term of a $2\times2$ matrix?
This can be even be done for en.wikipedia.org/wiki/Split-complex_number, see math.stackexchange.com/questions/3510/…
Feb
11
comment Why is the imaginary part of the logarithm of the gamma function a square wave?
You are right. The definition of the logarithm for negative values in Mathematica is simply $Im(\log(x))=\pi$ for $x<0$ and $0$ for $x>0$$, see also wolframalpha.com/input/?i=plot+log%5Bx%5D+x%2C+-10%2C+10 . I simply didn't expect such a step in the definition of the logarithm.
Feb
9
comment Why is the imaginary part of the logarithm of the gamma function a square wave?
Ok, the gamma function has poles. This explains maybe the period of the square wave. But why is the imaginary part of the logarithm of the Gamma function a constant (0 or $\pi$) between the poles so that one sees a square wave?
Feb
5
comment What's the connection between the Laplace transform and the Fourier transform?
It seems the Laplace transform given by the LCT is the bilateral Laplace transform or two-sided Laplace transform (en.wikipedia.org/wiki/Two-sided_Laplace_transform).
Jan
26
comment Relationship between Levi-Civita symbol and Grassmann numbers?
Wouldn't it then be much less confusing to call these $\theta_i$s "Grassmann vectors" instead of "Grassmann numbers"?
Jan
24
comment Relationship between Levi-Civita symbol and Grassmann numbers?
Ok. But then isn't the product $\theta_i\theta_j$ a tensor (more precisely a pseudotensor, since it anticommutes)?
Jan
24
comment Relationship between Levi-Civita symbol and Grassmann numbers?
Do I get this right: The notation of a Grassmann number like $\theta_i$ does not imply that $\theta$ is a vector with $i$ components. Instead $\theta_i$ is a scalar number like e.g. the imaginary number $i$, correct? So the product of two Grassmann numbers $\theta_i\theta_j$ is not an outer product of two vectors, but just a product of two scalars.
Apr
10
comment complex numbers and 2x2 matrices
Should we not have $a^2+b^2 \ge 0$, because the absolute value of a complex number cannot be smaller than zero?
Apr
9
comment What does it mean to multiply a real matrix by a complex scalar?
I'm confused about the sentence "Multiplication with a fixed complex number is a linear transformation on this two-dimensional vector space". I thought that a complex number itself (not only the multiplication operation) can be represented as a 2x2 matrix, see en.wikipedia.org/wiki/…. Doesn't that mean that the complex numbers are not a vector space, but a matrix space over the real numbers?
Oct
27
comment To “subtract” two matrices with different dimensions in Octave (Matlab)
This works also in Octave 3.4
Oct
27
comment To “subtract” two matrices with different dimensions in Octave (Matlab)
In Octave (3.4) this gives an error: a - b error: operator -: nonconformant arguments (op1 is 4x2, op2 is 1x2)
May
20
comment Does my definition of double complex noncommutative numbers make any sense?
@QiaochuYuan Thank you. "One cannot invent useful things, one can only rediscover them." ;-)
May
20
comment Does my definition of double complex noncommutative numbers make any sense?
Is there a special name for quaternions which have the coefficient of $k$ set to zero? And can't there also be quintions which could then factorize $a^2+b^2+c^2+d^2+e^2$ into two factors ?