From f0b633de6a7f445b6b93c16766a7473495c4e7ec Mon Sep 17 00:00:00 2001
From: Kevin Zakka <zakka@google.com>
Date: Mon, 20 May 2024 23:47:38 -0700
Subject: [PATCH] Fix typos in `least_squares` notebook.

PiperOrigin-RevId: 635696410
Change-Id: Iba9a2c8f121ca4994678ba933e19dce5323da27b
---
 python/least_squares.ipynb | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/python/least_squares.ipynb b/python/least_squares.ipynb
index ed3b8063..80819e91 100644
--- a/python/least_squares.ipynb
+++ b/python/least_squares.ipynb
@@ -2179,7 +2179,7 @@
    "source": [
     "### Non-quadratic norms\n",
     "\n",
-    "As explained in the background section, Least Squares can be generalized to norms other than the quadratic. We are now in a position to show how to define a non-quadratic norm, which is important in the estimation and system-identification contexts, where long-taled, disturbance-rejecting distributions are proportional to the exponent of a non-quadratic function.\n",
+    "As explained in the background section, Least Squares can be generalized to norms other than the quadratic. We are now in a position to show how to define a non-quadratic norm, which is important in the estimation and system-identification contexts, where long-tailed, disturbance-rejecting distributions are proportional to the exponent of a non-quadratic function.\n",
     "\n",
     "Let's say that we wish the task residual i.e., the vector from the hand to the target, to be evaluated with the \"Smooth L2\" function $c(r)$ which, for a given smoothing radius $d \\gt 0$ is\n",
     "$$\n",
@@ -2193,7 +2193,7 @@
     "H &=\\tfrac{\\partial^2 c}{\\partial r^2} = \\frac{I_{n_r} - g\\cdot g^T}{s}\n",
     "\\end{align}\n",
     "$$\n",
-    "There is no particularly good reason to use this norm for this optimization task, it is meerly an example.\n",
+    "There is no particularly good reason to use this norm for this optimization task, it is merely an example.\n",
     "\n",
     "Let's read the documentation of the `minimize.Norm` class:\n"
    ]
@@ -2215,7 +2215,7 @@
     "id": "3JGpR47DQ9S2"
    },
    "source": [
-    "Our sensors are 3 `r_pos` residual values for the hand-to-object vector followed by 21 `r_torque` actuator torques, for a total of `ns = 24` sensors. These are concatented for the entire trajectory, leading to a residual of size `24*N`, where `N` is the number of timesteps in a trajectory. After reshaping and slicing appropriately, the norm implementation looks like"
+    "Our sensors are 3 `r_pos` residual values for the hand-to-object vector followed by 21 `r_torque` actuator torques, for a total of `ns = 24` sensors. These are concatenated for the entire trajectory, leading to a residual of size `24*N`, where `N` is the number of timesteps in a trajectory. After reshaping and slicing appropriately, the norm implementation looks as follows:"
    ]
   },
   {
@@ -2291,7 +2291,7 @@
     "id": "J0brs9pG0-8Y"
    },
    "source": [
-    "Now that we are confident of our implemetation, we can see what the solution looks like:"
+    "Now that we are confident in our implemetation, we can see what the solution looks like:"
    ]
   },
   {