Show that the eigenvalues of a unitary matrix have modulus $1$
However, an interesting thing is that you can perhaps stop at the third last step, because an equivalent condition of a unitary matrix is that its eigenvector lies on the unit circle, so therefore, has magnitude 1.

1-1+1-1+1-1+1... 这个无穷数列的值是什么？如何证明？ - 知乎
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如何证明数学等式 1 + 1 = 2 的成立？ - 知乎
這裡對 陳浩 的答案作補充，在定義完加法後要證明一個定理，即下文截圖的定理3，說明加法是 well-defined,well-defined的含義是指確實存在一個函數＋滿足（＊）式，若沒有此定理，1＋1這樣的式子的含義就會不明確，所以在證1＋1＝2以前必須先證此定理，很明顯這個定理的證明要比1＋1＝2的證明要難 ...

Inverse of the sum of matrices - Mathematics Stack Exchange
The technique is useful in computation, because if the values in A and B can be very different in size then calculating 1 A+B 1 A + B $\frac{1}{A+B}$ according to (3) (3)

Why is $1/i$ equal to $-i$? - Mathematics Stack Exchange
That notation holds in general. For example, $2^{-1}=\frac{1}{2}$ since $\frac{1}{2}$ is the number that gives $1$ when multiplied by $2$. That notation holds in general. For example, $2^ {-1}=\frac {1} {2}$ since $\frac {1} {2}$ is the number that gives $1$ when multiplied by $2$. Share Cite answered May 11, 2015 at 12:16 Daniel 7,25552951 ...

Is the square root of -1 rational? - Mathematics Stack Exchange
$\sqrt{-1}=i$ is an imaginary number, not lying anywhere on the real number line. Therefore as others have said, it is neither rational nor irrational in the usual senses of those words.

complex numbers - How to prove $|z_1-z_2| \geq |z_1|-|z_2|$ in other ...
How to prove $|z_1-z_2| \\geq |z_1|-|z_2|$ in other way than this? I mean I tried to find on the internet but could not find. I ask for more straighforward way than the proof that is presented for i...

functional analysis - How are $C^0,C^1$ norms defined - Mathematics ...
How are $C^0,C^1$ norms defined? I know $L_p,L_\infty$ norms but are the former defined.

Using the definition of a limit to prove 1/n converges to zero.
Now: if you want to show 1 n → 0, then you should be able to do this. How close do you want to be to 0? Let's say you want to be "precise": you want to get within 0.0001 of 0. But you know 0.0001 = 1 10000, and so any term further along in the sequence than a10000 will be closer to 0 than 0.0001. But you can always do better!

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