diff --git a/src/3_vectors_spaces.md b/src/3_vectors_spaces.md index a4ef63259fa5c7348ad26a56937543e0ca8fe898..21961828c89b289b2e7b52430b6012d17fe0ce3b 100644 --- a/src/3_vectors_spaces.md +++ b/src/3_vectors_spaces.md @@ -20,20 +20,20 @@ A vector $\vec{v}$ is essentially a mathematical object characterised by both We can express a vector in terms of its individual **components**. - \item Let's assume we have an $n$-dimensional space, meaning that the vector $\vec{v}$ can be oriented + Let's assume we have an $n$-dimensional space, meaning that the vector $\vec{v}$ can be oriented in different ways along each of $n$ dimensions. - % + The expression of $\vec{v}$ in terms of its components is - \be + $$ \vec{v} = \lp v_1, v_2, \ldots, v_n\rp \, , - \ee + $$ - We will denote by ${\mathcal V}^n$ the {\bf vector space} composed + We will denote by ${\mathcal V}^n$ the **vector space** composed by all possible vectors of the above form. - % + Shortly we will define more precisely what are the mathematical properties of such space. - The components of a vector, $\{ v_i\}$ can be {\bf real numbers} or {\bf complex numbers}, + The components of a vector, $\{ v_i\}$ can be **real numbers** or **complex numbers**, depending on whether we have a real or a complex vector space. \item The expression above of $\vec{v}$ in terms of its components assume that we are