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Introduction to Linear Algrebra
​3Blue1Brown​
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 https://github.com/cben/mathdown/wiki/math-in-markdown​
​https://faculty.math.illinois.edu/~hildebr/tex/course/intro2.html​
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a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
α+β+δ+θ+ϕρ\alpha + \beta +\delta+\theta +\phi \rhoα+β+δ+θ+ϕρ
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Consider (eq:a):
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​
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$ \alpha = \beta $        (a)
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@equation(id)x=∑i=1Ni@/@equation(id)
x = \sum_{i=1}{N} i
@/@equation(id)x=i=1∑​Ni@/
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@equation(id)
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x = \sum_{i=1}{N} i
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@/
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 $ y=\sum_{i=1}^n g(x_i) $
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(a+b)3=(a+b)2(a+b)=(a2+2ab+b2)(a+b)=(a3+2a2b+ab2)+(a2b+2ab2+b3)=a3+3a2b+3ab2+b3\begin{align} 
(a+b)^3 &= (a+b)^2(a+b)\\
&=(a^2+2ab+b^2)(a+b)\\
&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
&=a^3+3a^2b+3ab^2+b^3
\end{align}
(a+b)3​=(a+b)2(a+b)=(a2+2ab+b2)(a+b)=(a3+2a2b+ab2)+(a2b+2ab2+b3)=a3+3a2b+3ab2+b3​​
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\begin{align} 
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(a+b)^3 &= (a+b)^2(a+b)\\
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&=(a^2+2ab+b^2)(a+b)\\
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&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
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&=a^3+3a^2b+3ab^2+b^3
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\end{align}
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​
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\[
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\left|\sum_{i=1}^n a_ib_i\right|
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\le
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\left(\sum_{i=1}^n a_i^2\right)^{1/2}
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\left(\sum_{i=1}^n b_i^2\right)^{1/2}
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\]
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