From 9a9aec1118d15f4f85ff66d0c0709c5707a8b650 Mon Sep 17 00:00:00 2001 From: austinwn Date: Fri, 9 May 2014 16:14:32 -0500 Subject: [PATCH] Added missing transpose --- 12.4.2 The Power Method.ipynb | 2 +- 12.5.1 The Inverse Power Method.ipynb | 2 +- 12.5.2 Shifting the Inverse Power Method.ipynb | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/12.4.2 The Power Method.ipynb b/12.4.2 The Power Method.ipynb index b0ca03d..ab5a770 100644 --- a/12.4.2 The Power Method.ipynb +++ b/12.4.2 The Power Method.ipynb @@ -128,7 +128,7 @@ " \n", " \n", "If you change the \"3\" on the diagonal to \"-4\", then you have two largest eigenvalues (in magnitude), and the vector $ x $ will end up in the space spanned by $ v_0 $ and $ v_1 $. \n", - " You can check this by looking at $ ( I - V_L ( V_L^T V_L )^{-1} V_L ) x $, where $V_L $ equals the matrix with $ v_0 $ and $ v_1 $ as its columns, to see if the vector orthogonal to $ {\\cal C}( V_L ) $ converges to zero. This is seen in the following code block:\n", + " You can check this by looking at $ ( I - V_L ( V_L^T V_L )^{-1} V_L^T ) x $, where $V_L $ equals the matrix with $ v_0 $ and $ v_1 $ as its columns, to see if the vector orthogonal to $ {\\cal C}( V_L ) $ converges to zero. This is seen in the following code block:\n", "\n" ] }, diff --git a/12.5.1 The Inverse Power Method.ipynb b/12.5.1 The Inverse Power Method.ipynb index c1a1dfe..04d0468 100644 --- a/12.5.1 The Inverse Power Method.ipynb +++ b/12.5.1 The Inverse Power Method.ipynb @@ -156,7 +156,7 @@ " \n", " Try changing the \"2\" to a \"-1\" or \"1\". What happens then?\n", " \n", - " You can check this by looking at $ ( I - V_R ( V_R^T V_R )^{-1} V_R ) x $, where $V_R $ equals the matrix with $ v_2 $ and $ v_3 $ as its columns, to see if the vector orthogonal to $ {\\cal C}( V_R ) $ converges to zero. This is seen in the following code block:\n" + " You can check this by looking at $ ( I - V_R ( V_R^T V_R )^{-1} V_R^T ) x $, where $V_R $ equals the matrix with $ v_2 $ and $ v_3 $ as its columns, to see if the vector orthogonal to $ {\\cal C}( V_R ) $ converges to zero. This is seen in the following code block:\n" ] }, { diff --git a/12.5.2 Shifting the Inverse Power Method.ipynb b/12.5.2 Shifting the Inverse Power Method.ipynb index 974dd24..9044898 100644 --- a/12.5.2 Shifting the Inverse Power Method.ipynb +++ b/12.5.2 Shifting the Inverse Power Method.ipynb @@ -165,7 +165,7 @@ " \n", " This time, if you change the \"2\" on the diagonal to \"-1\", you still converge to $ v_{n-1} $ because for the matrix $ A - \\mu I $, $ -1 - \\mu $ is not as small as $ 1 - \\mu $ (in magnitude).\n", "\n", - " You can check this by looking at $ ( I - V_R ( V_R^T V_R )^{-1} V_R ) x $, where $V_R $ equals the matrix with $ v_2 $ and $ v_3 $ as its columns, to see if the vector orthogonal to $ {\\cal C}( V_R ) $ converges to zero. This is seen in the following code block:\n" + " You can check this by looking at $ ( I - V_R ( V_R^T V_R )^{-1} V_R^T ) x $, where $V_R $ equals the matrix with $ v_2 $ and $ v_3 $ as its columns, to see if the vector orthogonal to $ {\\cal C}( V_R ) $ converges to zero. This is seen in the following code block:\n" ] }, {