Corrected typos week 1

Author: Marius Hope

doc/pub/week1/ipynb/week1.ipynb

@@ -659,7 +659,7 @@
    "id": "f60e43ec",
    "metadata": {},
    "source": [
-    "For two arbitrary vectors $\\vert x\\rangle$ and $\\vert y\\rangle$ with the same lentgh, we have the\n",
+    "For two arbitrary vectors $\\vert x\\rangle$ and $\\vert y\\rangle$ with the same length, we have the\n",
     "general expression"
    ]
   },
@@ -1414,7 +1414,7 @@
    "metadata": {},
    "source": [
     "## Examples of tensor products\n",
-    "If we now go back to our original one-qubit basis states, we can form teh following tensor products"
+    "If we now go back to our original one-qubit basis states, we can form the following tensor products"
    ]
   },
   {
@@ -1981,7 +1981,7 @@
     "\n",
     "Since our original basis $\\vert \\psi\\rangle$ is orthogonal and normalized with $\\vert\\alpha\\vert^2+\\vert\\beta\\vert^2=1$, the new basis is also orthogonal and normalized, as we can see below here.\n",
     "\n",
-    "Since the inverse of a hermitian matrix is equal to its hermitian\n",
+    "Since the inverse of a unitary matrix is equal to its hermitian\n",
     "conjugate/adjoint), unitary transformations are always reversible.\n",
     "\n",
     "Why are only unitary transformations allowed? The key lies in the way the inner product tranforms.\n",
@@ -2004,7 +2004,7 @@
    "id": "1d1c60c1",
    "metadata": {},
    "source": [
-    "or in terms of a matrix-vector notatio we have"
+    "or in terms of a matrix-vector notation we have"
    ]
   },
   {