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Scalar value is notated by not-bold lower case.
Multiplication of vector by scalar value:
$$$y=ax=\begin{bmatrix} ax_{1}\\ax_{2}\\...\\ax_{N} \end{bmatrix}$$$
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Inner product when 2 vectors have 0 angle :
$$$c=\langle x,y \rangle=x\cdot y=x^{T}y=\sum\limits_{t=1}^{N}x_{t}y_{t}$$$
Result value of inner product is one scalar value in real number.
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When result of inner product is 0,
you can say 2 vectors are perpendicular.
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Inner product when 2 vectors have angle:
$$$c=||x||||y||\cos{\theta}$$$
$$$0<\theta<\pi$$$