From d3827df7dbd17d31aadea47dda2e5c0fc055d70b Mon Sep 17 00:00:00 2001
From: Maciej Topyla <m.m.topyla@student.tudelft.nl>
Date: Sun, 4 Sep 2022 11:36:26 +0000
Subject: [PATCH] latex fix
---
src/3_vector_spaces.md | 14 +++++++-------
1 file changed, 7 insertions(+), 7 deletions(-)
diff --git a/src/3_vector_spaces.md b/src/3_vector_spaces.md
index 0b86d44..e380fd2 100644
--- a/src/3_vector_spaces.md
+++ b/src/3_vector_spaces.md
@@ -82,17 +82,17 @@ solution proces.
You might be already familiar with the concept of performing a number of various **operations** between vectors, so in this course, let us review some essential operations that are relevant to start working with quantum mechanics:
!!! info "Addition"
- I can add two vectors to produce a third vector, $$\vec{a} + \vec{b}= \vec{c}$$.
- As with scalar addition, also vectors satisfy the commutative property, $$\vec{a} + \vec{b} = \vec{b} + \vec{a}$$.
+ I can add two vectors to produce a third vector, $$\vec{a} + \vec{b}= \vec{c}.$$
+ As with scalar addition, also vectors satisfy the commutative property, $$\vec{a} + \vec{b} = \vec{b} + \vec{a}.$$
Vector addition can be carried out in terms of their components,
- $$ \vec{c} = \vec{a} + \vec{b} = (a_1 + b_1, a_2 + b_2, \ldots, a_n + b_n) = (c_1, c_2, \ldots, c_n) \, .$$
+ $$ \vec{c} = \vec{a} + \vec{b} = (a_1 + b_1, a_2 + b_2, \ldots, a_n + b_n) = (c_1, c_2, \ldots, c_n).$$
!!! info "Scalar multiplication"
- I can multiply a vector by a scalar number (either real or complex) to produce another vector, $$\vec{c} = \lambda \vec{a}$$.
+ 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. $(\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a}$
+ $$1. \vspace{5pt} (\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})$$
+ $$2. \vspace{5pt} \lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}$$
+ $$3. \vspace{5pt} (\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a}$$
!!! info "Vector product"
In addition to multiplying a vector by a scalar, as mentioned above, one can also multiply two vectors among them.
--
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