
What does $QAQ^{-1}$ actually mean? - Mathematics Stack …
2020年4月28日 · Let me provide some context. I was specifically looking at the application of linear algebra to the stress tensor $\sigma$ and how we get the transformed stress state in some rotated coordinate system by the following multiplication: $\sigma'=Q\sigma Q^{-1}(Q$ is a rotation matrix defined by the angle we want to rotate the axes).
What is the value of $1^i$? - Mathematics Stack Exchange
2010年8月30日 · There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm. The confusing point here is that the formula $1^x = 1$ is not part of the definition of complex exponentiation, although it is an immediate consequence of the definition of natural number exponentiation.
Formal proof for $(-1) \\times (-1) = 1$ - Mathematics Stack …
The Law of Signs $\rm\: (-x)(-y) = xy\:$ isn't normally assumed as an axiom. Rather, it is derived as a consequence of more fundamental Ring axioms $ $ [esp. the distributive law $\rm\,x(y+z) = xy + xz\,$], laws which abstract the common algebraic structure shared by …
If $A A^{-1} = I$, does that automatically imply $A^{-1} A = I$?
2020年3月30日 · A-1 A means that first we apply A transformation then we apply A-1 transformation. When we apply A transformation we reach some plane having some different basis vectors but after apply A-1 we again reach to the plane have basis i ^ (0,1) and j ^ (1,0). It means that after applying A-1 we reach to the transformation which does nothing.
power series - How can we know the answer to 1-1+1-1+1 ...
Summing to infinity cannot truly be evaluated as a sum as it is a process of addition that never ends, rather than a final result. What we can say fairly categorically is that the only acceptable numerical answers are $1, 0,$ and $\frac{1}{2}$.
Why is $1/i$ equal to $-i$? - Mathematics Stack Exchange
2015年5月11日 · There are multiple ways of writing out a given complex number, or a number in general. Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ for example.
Formula for $1^2+2^2+3^2+...+n^2$ - Mathematics Stack …
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Proof that $(AA^{-1}=I) \\Rightarrow (AA^{-1} = A^{-1}A)$
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abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange
2013年1月15日 · The main reason that it takes so long to get to $1+1=2$ is that Principia Mathematica starts from almost nothing, and works its way up in very tiny, incremental steps. The work of G. Peano shows that it's not hard to produce a useful set of axioms that can prove 1+1=2 much more easily than Whitehead and Russell do.
General term formula of series 1/1 + 1/2 + 1/3 ... +1/n
$$\ln(n+1)\le\sum_{i=1}^n\frac1i\le\ln(n)+1$$ This is a rather tight upper limit and lower limit you can use to approximate your answer. One could also note that $$\sum_{i=1}^n\frac1i=\int_0^1\sum_{i=0}^{n-1}x^i\ dx=\int_0^1\frac{1-x^n}{1-x}\ dx$$ We also have the Euler-Maclaurin expansion: