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Commit c5012e6c authored by Maciej Topyla's avatar Maciej Topyla
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Update src/3_vector_spaces.md

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......@@ -90,9 +90,9 @@ You might be already familiar with the concept of performing a number of various
!!! info "Scalar multiplication"
I can multiply a vector by a scalar number (either real or complex) to produce another vector, $$\vec{c} = \lambda \vec{a}.$$
Addition and scalar multiplication of vectors are both *associative* and *distributive*, so the following relations hold
$$1. \hspace{5pt} (\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})$$
$$2. \hspace{5pt} \lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}$$
$$3. \hspace{5pt} (\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a}$$
$$\begin{align} &1. \qquad (\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})\\
&2. \qquad \lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}\\
&3. \qquad (\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a} \end{align}$$
### Vector products
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