论文标题
所有2x2真实矩阵的交互式可视化，并应用于传达迭代特征值算法的动力学
An interactive visualisation for all 2x2 real matrices, with applications to conveying the dynamics of iterative eigenvalue algorithms
论文作者
论文摘要
我们提出了2x2真矩阵的两个交互式可视化，我们称为V1和V2。 V1仅对PSD矩阵有效，并以微不足道的方式使用光谱定理 - 我们将其用作热身。相比之下，V2适用于 *所有 * 2x2真实矩阵，并且基于鲜为人知的Lie Sphere几何理论。我们表明，可以使用两者都可以说明迭代特征值算法的动力学。 V2具有同时描述矩阵的许多特性的优点，所有这些特性都与特征值算法的研究有关。 V2可以描绘的矩阵属性的示例是其Jordan正常形式和正交相似性类别，以及它是三角形，对称还是正交的。尽管具有丰富的性能，但使用v2可以交互作用似乎很直观。
We present two interactive visualisations of 2x2 real matrices, which we call v1 and v2. v1 is only valid for PSD matrices, and uses the spectral theorem in a trivial way -- we use it as a warm-up. By contrast, v2 is valid for *all* 2x2 real matrices, and is based on the lesser known theory of Lie Sphere Geometry. We show that the dynamics of iterative eigenvalue algorithms can be illustrated using both. v2 has the advantage that it simultaneously depicts many properties of a matrix, all of which are relevant to the study of eigenvalue algorithms. Examples of the properties of a matrix that v2 can depict are its Jordan Normal Form and orthogonal similarity class, as well as whether it is triangular, symmetric or orthogonal. Despite its richness, using v2 interactively seems rather intuitive.
