fix admonitions

src/3_vector_spaces.md

@@ -90,28 +90,26 @@ 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. $(\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})$
   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
-the other where the end result is another vectors. 
-
-- The **scalar production of vectors** is given by $$ \vec{a}\cdot \vec{b} = a_1b_1 + a_2b_2 + \ldots + a_nb_n \, .$$
-Note that since the scalar product is just a number, its value will not depend on the specific
-basis in which we express the vectors: the scalar product is said to be *basis-independent*. The scalar product is also found via
-$$\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}| \cos \theta$$
-with $\theta$ the angle between the vectors.
-
-- The **vector product** (or cross product) between two vectors $\vec{a}$ and $\vec{b}$ is given by
-$$
-\vec{a}\times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \hat{n} \, ,
-$$
-where $|\vec{a}|=\sqrt{ \vec{a}\cdot\vec{a} }$ (and likewise for $|\vec{b}|$) is the norm of the vector $\vec{a}$, $\theta$ is the angle
-between the two vectors, and $\hat{n}$ is a unit vector which is *perpendicular* to the plane that contains $\vec{a}$ and $\vec{b}$. 
-Note that this cross-product can only be defined in *three-dimensional vector spaces*. The resulting vector $\vec{c}=\vec{a}\times \vec{b} $ will have as components $c_1 = a_2b_3-a_3b_2$, $c_2= a_3b_1 - a_1b_3$, and $c_3= a_1b_2 - a_2b_1$.
+!!! info "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 the other where the end result is another vectors. 
+
+!!! info "The scalar production of vectors" 
+  The **scalar production of vectors is given by $$ \vec{a}\cdot \vec{b} = a_1b_1 + a_2b_2 + \ldots + a_nb_n \, .$$
+  Note that since the scalar product is just a number, its value will not depend on the specific
+  basis in which we express the vectors: the scalar product is said to be *basis-independent*. The scalar product is also found via 
+  $$\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}| \cos \theta$$ with $\theta$ the angle between the vectors.
+
+!!! info "Cross product"
+  "The vector product (or cross product) between two vectors $\vec{a}$ and $\vec{b}$ is given by 
+  $$ \vec{a}\times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \hat{n}$$
+  where $|\vec{a}|=\sqrt{ \vec{a}\cdot\vec{a} }$ (and likewise for $|\vec{b}|$) is the norm of the vector $\vec{a}$, $\theta$ is the angle between the two vectors, and $\hat{n}$ is a unit vector which is *perpendicular* to the plane that contains $\vec{a}$ and $\vec{b}$. 
+  Note that this cross-product can only be defined in *three-dimensional vector spaces*. The resulting vector 
+  $\vec{c}=\vec{a}\times \vec{b} $ will have as components $c_1 = a_2b_3-a_3b_2$, $c_2= a_3b_1 - a_1b_3$, and $c_3= a_1b_2 - a_2b_1$.
 
 - A special vector is the **unit vector**, which has a norm of 1 *by definition*. A unit vector is often denoted with a hat, rather than an arrow ($\hat{i}$ instead of $\vec{i}$). To find the unit vector in the direction of an arbitrary vector $\vec{v}$, we divide by the norm: 
 $$\hat{v} = \frac{\vec{v}}{|\vec{v}|}$$