15第十五次课用初等变换法化二次型为标准形正定二次型.ppt

第十五次课 掌握用正交变换法化二次型为标准形的方法 了解惯性定理 了解正定二次型、正定矩阵的概念及他们的判别法 教学内容 教学目标及基本要求 §6.4 正定二次型 §6.3 用初等变换法化二次型为标准形 正交变换化二次型为标准形 重 点 难 点 正交变换化二次型为标准形 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1、二次型的标准形不唯一。 2、 即： 标准形中平方项的项数为 设 经适当的满秩线性变换 化为标准形： 是 的秩 惯性定理 (P172) §6.3 用初等变换法化二次型为标准形 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 则再作一次满秩变换： 可得二次型的规范形： 3、惯性定理： 满秩变换化为规范二次型，且规范性是唯一的。 元实二次型 都存在 negative index of inertia positive index of inertia signature normal form of a quadratic form law of inertia Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. §6.4 正定二次型 一、基本概念 (P173定义6.4.1) indefinite quadratic form positive(negative) semidefinite matrix positive(negative) definite matrix Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二、判定 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 顺序主子式负、正相间 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例1 (P175例6.4.2) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 小 结 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 提前预习 作 业 习题6(A)： 总复习 ，判断二次型是否正定 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.