From db8023cb1d46a984c09823d7585ffafb63777f8c Mon Sep 17 00:00:00 2001 From: "Steven G. Johnson" Date: Wed, 20 Mar 2024 13:56:57 -0400 Subject: [PATCH] Update Circulant-Matrices.ipynb: fix image link --- lectures/Circulant-Matrices.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lectures/Circulant-Matrices.ipynb b/lectures/Circulant-Matrices.ipynb index 72d3c50a..fa13d324 100644 --- a/lectures/Circulant-Matrices.ipynb +++ b/lectures/Circulant-Matrices.ipynb @@ -137,7 +137,7 @@ "\n", "In this lecture, I want to introduce you to a new type of matrix: **circulant** matrices. Like Hermitian matrices, they have orthonormal eigenvectors, but unlike Hermitian matrices we know *exactly* what their eigenvectors are! Moreover, their eigenvectors are closely related to the famous Fourier transform and Fourier series. Even more importantly, it turns out that circulant matrices and the eigenvectors lend themselves to **incredibly efficient** algorithms called FFTs, that play a central role in much of computational science and engineering.\n", "\n", - "![a ring of springs](https://github.com/stevengj/1806-spring17/raw/master/lectures/cyclic-springs.png) \n", + "![a ring of springs](https://raw.githubusercontent.com/mitmath/1806/spring17/lectures/cyclic-springs.png) \n", "\n", "Consider a system of $n$ identical masses $m$ connected by springs $k$, sliding around a *circle* without friction. Similar to lecture 26, the vector $\\vec{s}$ of displacements satifies $m\\frac{d^2\\vec{s}}{dt^2} = -kA\\vec{s}$, where $A$ is the $n \\times n$ matrix:\n", "\n",