谱定理(Spectral Theorem)是线性代数与泛函分析中的核心定理,描述了自伴算子(如对称矩阵、埃尔米特矩阵等)通过特征分解实现对
谱定理(Spectral Theorem) 谱定理在线性代数里可以这样表述 \boldsymbol{A}是正规矩阵当且仅当存在酉矩阵\boldsymbol{U},使得 \boldsymbol{A}=\boldsymbol{U \Lambda U}^* \tag{2} 其中\boldsymbol{\Lambda}为对角阵。 结合特征值分解和酉矩阵的定义,不难发现(2)其实就是一种特殊的特征值分解\boldsymbol...
It is no exaggeration to say that symmetric matrices S are the most import matrices the world will ever see in the theory of linear algebra and also in the applications. Spectral Theorem是关于实对称矩阵的一个定理,描述如下: 任何一个n阶实对称矩阵S,都可以被分解成一个很漂亮的形式QΛQ⊤。Q...
内容提示: 3Spectral TheoremThe Spectral Theorem is a milestone in the theory of Hilbert space operators,providing a full statement about the nature and structure of normal operators.For compact normal operators the Spectral Theorem can be completely inves-tigated without requiring any knowledge of ...
谱定理（Spectral Theorem）谱定理在线性代数里可以这样表述：正规矩阵A当且仅当存在酉矩阵U，使得U⁻¹AU = D，其中D为对角阵。结合特征值分解和酉矩阵的定义，不难发现D其实就是一种特殊的特征值分解A = PDP⁻¹，U = P。证明必要性 若U⁻¹AU = D，其中...
泛泛来讲，谱定理给出了算子或者矩阵可以对角化的条件（也就是可以在某个基底中用对角矩阵来表示）。对角化的概念在有限维空间中比较直接，但是对于无穷维空间中的算子需要作一些修改。通常，谱定理辨认出一族可以用乘法算子来代表的线性算子，这是可以找到的最简单的情况了。用更抽象的语言来讲，谱定理...
The main part of this chapter will be devoted to the proof of a theorem on the expansion of an arbitrary family of commuting unbounded (in general) normal operators in generalized joint eigenvectors (the "spectral projection theorem"). This theorem singles out "projectors" on the generalized ...
The Spectral Theorem For the final topic in this course, we combine our work in Chapter 5 (on diagonalization) with our work in Chapter 6 (on inner product spaces). We have seen that a linear operator T on a finite-dimensional vector space V is diagonalizable if and only if V has...
Spectral theorem Jump to navigationJump to search Then you will have no problem growing taller, your level of persistence is very high. I didn't believe my playing partner when he said I couldn't clear it now because I didn't have a club in my bag that I could make it with. Only ...
在探讨线性代数的领域里，对称矩阵无疑占据了核心地位，其在理论与应用中的重要性不言而喻。Gilbert Strang对此的评价绝非过誉。实对称矩阵S的Spectral Theorem揭示了其独特的分解特性。任意阶实对称矩阵S均可表示为一个简洁的对角形式S=QΛQT。其中，Q是构成由S下的n个orthonormal vectors（标准正交基）...