# Linear Functions

In function notation $$f: \mathbf{R}^n \to \mathbf{R}$$ means that $$f$$ is a function that maps real $$n$$-vectors to real numbers, it is a scalar-valued function of $$n$$-vectors. In other words, if $$x$$ is an $$n$$-vector, then $$f(x)$$, which is a scalar, denotes the value of $$f$$ at $$x$$. That is, $$f$$ returns a real number. Furthermore, we can interpret $$f$$ as a function of $$n$$ scalar arguments, as in …

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# 1% Rule

The 1% rule is a trading risk management technique that instructs the trader to never risk more than 1% of their account on any given trade. This article from the Balance tries to give some examples but it lost me at “By risking 1 percent of your account on a single trade, you can make a trade which gives you a 2-percent return on your account, even though the market only moved a fraction of a percent. …

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# Juking For Linux

A very long time ago, I was a Windows user. I didn’t know any better. I even used Android. Those environments never sat well with me. Eventually, I “upgraded” into the Apple ecosystem, which although cohesive—as in, things just works—was too insular. The Microsoft, Apple, and Google triumvirate is not one that I’m fond of. Three times already, I tried to crossover into the Linux world. Three times I was thwarted by my own inexperience and incompetence. …

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# Inner Product

The inner-product (also called dot-product) of two $$n$$-vectors is defined as the scalar $a^Tb = a_1b_1 + a_2b_2 + \cdots + a_nb_n$ the sum of the products of corresponding entries. The $$T$$ stands for transpose and we’ll tackle it another time. The dot product has other notations as well, such as $$\langle a, b \rangle$$, $$\langle a | b \rangle$$, $$(a, b)$$, $$a \cdot b$$. As an example $\begin{bmatrix} -1 \\ 2 \\ 2 \end{bmatrix}^T \begin{bmatrix} 1 \\ 0 \\ -3 \end{bmatrix} = (-1)(1) + (2)(0) + (2)(-3) = -7$ …

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# Scalar-Vector Multiplication

Scalar multiplication (or scalar-vector multiplication) is an operation in which a vector is multiplied by a scalar (i.e., number), which is done by multiplying every element of the vector by the scalar. $(-2) \begin{bmatrix} 1 \\ 9 \\ 6 \end{bmatrix} = \begin{bmatrix} -2 \\ -18 \\ -12 \end{bmatrix}$ Similar notation is $$a/2$$, where $$a$$ is a vector, leading to $$(1/2)a$$. The scalar-vector product $$(-1)a$$ is simply $$-a$$. The scalar-vector $$0a = 0$$. …

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