diff --git a/src/4_vector_spaces_QM.md b/src/4_vector_spaces_QM.md
index 96bd4aab792c722f9210a434c2a952bb882f5005..2bdd85ee598377fc44481fc3c8bfdabf7bcd09ce 100644
--- a/src/4_vector_spaces_QM.md
+++ b/src/4_vector_spaces_QM.md
@@ -28,7 +28,7 @@ The contents of this lecture are summarised in the following **videos**:
 
 - [3. Finding expansion coefficients for Dirac notation](https://www.dropbox.com/s/k9plspkonnk3nc0/linear_algebra-07.mov?dl=0)
 
-**Total lenght of the videos: ~14 minutes**
+**Total length of the videos: ~14 minutes**
 
 ---
 
@@ -45,7 +45,7 @@ This vector space is known as the *state space* of the system.
 !!! info "Ket"
      A physical state of a quantum system is represented by a symbol $$|~~\rangle$$ known as a **ket**. 
      This notation is known as the *Dirac notation*, and it is very prominent in the description of quantum mechanics. 
-     Note that a *ket* is also refered to as a state vector, *ket* vector, or just a state. 
+     Note that a *ket* is also referred to as a state vector, *ket* vector, or just a state. 
 
 ### Hilbert space
 
@@ -72,7 +72,7 @@ The set of all possible state vectors describing a given physical system forms a
      $$\sum_{i=1}^n c_i |{\psi_i}\rangle=0\;\text{then}\; c_i=0\;\text{for all}\; i$$
 
 !!! info "Dimensionality"
-     The minimum number of vectors needed to form a complete set of basis states is known as the *dimensionality* of the state space. In quantum mechanis you will encounter systems whose Hilbert spaces have very different dimensionality, from the spin-1/2 particle (a $n=2$ vector space) to the free particle (whose state vectors live in an infinite vector space).
+     The minimum number of vectors needed to form a complete set of basis states is known as the *dimensionality* of the state space. In quantum mechanics you will encounter systems whose Hilbert spaces have very different dimensionality, from the spin-1/2 particle (a $n=2$ vector space) to the free particle (whose state vectors live in an infinite vector space).
 
 ### Bra vectors