diff --git a/src/3_vector_spaces.md b/src/3_vector_spaces.md index 67b79353bc5455d29124c3b3309115cd651f2364..b75e5d553a2a08dd6dfd04d42e374d13d48bfbe7 100644 --- a/src/3_vector_spaces.md +++ b/src/3_vector_spaces.md @@ -74,9 +74,9 @@ You might be familiar with the concept that one can perform a number of **operat Addition and scalar multiplication of vectors are both {\bf associative} and {\bf distributive}, so the following relations hold - - $$(\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})$$ - - $$\lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}$$ - - $$(\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a}$$ + 1. $$(\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})$$ + 2. $$\lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}$$ + 3. $$(\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a}$$ - **Vector product**: in addition to multiplying a vector by a scalar, as mentioned above, one can also multiply two vectors among them. There are two types of vector productions, one where the end result is a scalar (so just a number) and