Tagged Questions
1
vote
1answer
38 views
All the logarithms of a non-singular matrix.
I'm reading some notes on dynamical systems that talk about matrix logarithms with little to no detail on the subject. I read the wikipedia article and others on the internet, but not all is clear.
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0
votes
2answers
221 views
How to enter subscript characters in WolframAlpha? [closed]
I'm trying to enter equations like this in WolframAlpha.
How do I format this?
1
vote
1answer
81 views
Is $e^{\alpha\log(M)}$ equal to $M^{\alpha}$?
Supposing the matrix logarithm exists, is $e^{\alpha\log(M)}$ equal to $M^{\alpha}?$
This equality obviously holds for positive reals, but does it also hold for matrices?
3
votes
1answer
122 views
How to prove $\left\|\ln\left(e^{iH_1}e^{iH_2}\right)\right\|\leq\left\|H_1\right\|+\left\|H_2\right\|$?
Let $H_1$ and $H_2$ denote arbitrary Hermitian operators (finite dimensional) and let $\left\|\ldots\right\|$ denote the usual operator norm. I conjecture that
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3
votes
3answers
260 views
Value of Logarithm of negative number
Why the logarithmic value of negative number can't be define? Is there any special reason?
1
vote
4answers
64 views
Simplifing logarithmic equation
I have the result of a differential equation to be:
$$\ln(x+3)=3\ln(t+2)+C$$
I want this to be as simplified as possible. Can it be proceeded like:
$$e^{(x+3)}=3e^{(t+2)+C}$$
I am not sure about ...
0
votes
1answer
34 views
Specific range of numbers is given, trying to get another number within same range
I'm trying to calculate the width of an HTML element based on the window size.
Here's what I have. These width values (first value) accurately match with the width the HTML element must be (second ...
0
votes
1answer
166 views
How to learn graph plots of math functions?
I really don't know how to we say that a log function would look like this or polynomial function would look like this. I know that if I have like $X + Y = c$, I can draw straight line by taking ...
1
vote
1answer
106 views
Can you use a logarithm coefficient in a linear equation?
I have an equation that looks like $x+(\ln3)y+z=0$ where there's a natural logarithm as a coefficient. Is it possible to have this in a linear equation? I know that you cannot have a root or a product ...
5
votes
1answer
197 views
Can I build a program that will tell me if a real world data set looks linear, logarithmic, exponential etc?
I have a bunch of real world data sets and from manually plotting some of the data in graphs, I've discovered some data sets look pretty much logarithmic and some look linear, or exponential (and some ...
5
votes
2answers
339 views
Logarithm of a Markov Matrix
Start with a Markov matrix $\mathbf{M}$, whose elements are all between $0 \le \mathbf{M}_{ij} \le 1$ and each row sums to one. There is a natural connection with this matrix and the rate matrix ...
