HW1/Solutions_HW1.ipynb

@@ -132,7 +132,7 @@
         "\n",
         "$\\parallel UA \\parallel_{F} = \\sqrt{tr[(UA)^*(UA)]} = \\sqrt{tr[A^*U^*UA]}$.\n",
         "\n",
-        "Let us take advantage of the fact that $U$ is unitary, i.e. $U^*U = UU^*= I$. That:\n",
+        "Let us take advantage of the fact that $U$ is unitary, i.e. $U^*U = I$. That:\n",
         "\n",
         "$\\parallel UA \\parallel_{F} = \\sqrt{tr[A^*U^*UA]} = \\sqrt{tr[A^*A]} = \\parallel A \\parallel_{F}$\n",
         "\n",
@@ -141,7 +141,7 @@
         "$\\parallel AU \\parallel_{F} = \\sqrt{tr[(AU)^*(AU)]} = \\sqrt{tr[U^*A^*AU]}$.\n",
         "\n",
         "Let's use the trace property $tr(AB) = tr(BA)$. So:\n",
-        "$\\parallel AU \\parallel_{F} = \\sqrt{tr[U^*A^*AU]} = \\sqrt{tr[AUU^*A^*]} = \\sqrt{tr[AA^*]} = \\parallel A \\parallel_{F}$.\n",
+        "$\\parallel AU \\parallel_{F} = \\sqrt{tr[U^*A^*AU]} = \\sqrt{tr[A^*AUU^*]} = \\sqrt{tr[A^*A]} = \\parallel A \\parallel_{F}$.\n",
         "\n",
         "Thus $\\parallel UA \\parallel_{F} = \\parallel AU\\parallel_{F} = \\parallel A \\parallel_{F}$."
       ],