eigenvalue decomposition
特征值分解
eigenvalue equation
特征值方程
eigenvalue problem
特征值问题
Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.
每个可见特征值符合操作者一特征向量，而相关的特征值符合特征值里的可见值。
This paper discusses the structure, calculation of multiplication and power, eigenvalue and eigenvector, and diagonalizable problems of matrix of rank equal to 1.
摘要对秩等于1的矩阵的结构、乘法与乘幂运算、特征值与特征向量和对角化问题进行了讨论。
One kind of inverse eigenvalue problems, whose solutions are required to be normal or diagonalizable matrices, is investigated in quaternionic quantum mechanics.
摘要本文研究了四元数量子力学中一类要求其解是正规或可对角化四元数矩阵的特征值反问题。
In the practical applications of highly nonnormal matrices, these theorems may be more useful than their generalized eigenvalue special cases and may provide more descriptive information.
在对高度非正规矩阵的研究应用中，这些定理将比它们的特例-广义特征值定理更可靠，能提供更多的信息。
The eigenvalues of the matrix can be calculated using specialized algorithms.
矩阵的特征值可以使用专门的算法计算。
Eigenvalues play a crucial role in solving systems of linear equations.
特征值在解线性方程组中起着至关重要的作用。
Finding the eigenvalues of a matrix involves solving a characteristic equation.
找到矩阵的特征值涉及解特征方程。
Eigenvalues are used in various fields such as physics, engineering, and computer science.
特征值在物理学、工程学和计算机科学等领域中被广泛应用。
The eigenvalues of a symmetric matrix are always real numbers.
对称矩阵的特征值始终是实数。
Eigenvalues provide information about the behavior of a linear transformation.
特征值提供了关于线性变换行为的信息。
Eigenvalues are often used in principal component analysis for dimensionality reduction.
特征值在主成分分析中常用于降维。
The eigenvectors corresponding to distinct eigenvalues are linearly independent.
对应不同特征值的特征向量是线性无关的。
Eigenvalues and eigenvectors are fundamental concepts in linear algebra.
特征值和特征向量是线性代数中的基本概念。
The eigenvalues of a diagonal matrix are simply the diagonal entries.
对角矩阵的特征值就是对角线上的元素。
eigenvalue decomposition
特征值分解
eigenvalue equation
特征值方程
eigenvalue problem
特征值问题
Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.
每个可见特征值符合操作者一特征向量，而相关的特征值符合特征值里的可见值。
This paper discusses the structure, calculation of multiplication and power, eigenvalue and eigenvector, and diagonalizable problems of matrix of rank equal to 1.
摘要对秩等于1的矩阵的结构、乘法与乘幂运算、特征值与特征向量和对角化问题进行了讨论。
One kind of inverse eigenvalue problems, whose solutions are required to be normal or diagonalizable matrices, is investigated in quaternionic quantum mechanics.
摘要本文研究了四元数量子力学中一类要求其解是正规或可对角化四元数矩阵的特征值反问题。
In the practical applications of highly nonnormal matrices, these theorems may be more useful than their generalized eigenvalue special cases and may provide more descriptive information.
在对高度非正规矩阵的研究应用中，这些定理将比它们的特例-广义特征值定理更可靠，能提供更多的信息。
The eigenvalues of the matrix can be calculated using specialized algorithms.
矩阵的特征值可以使用专门的算法计算。
Eigenvalues play a crucial role in solving systems of linear equations.
特征值在解线性方程组中起着至关重要的作用。
Finding the eigenvalues of a matrix involves solving a characteristic equation.
找到矩阵的特征值涉及解特征方程。
Eigenvalues are used in various fields such as physics, engineering, and computer science.
特征值在物理学、工程学和计算机科学等领域中被广泛应用。
The eigenvalues of a symmetric matrix are always real numbers.
对称矩阵的特征值始终是实数。
Eigenvalues provide information about the behavior of a linear transformation.
特征值提供了关于线性变换行为的信息。
Eigenvalues are often used in principal component analysis for dimensionality reduction.
特征值在主成分分析中常用于降维。
The eigenvectors corresponding to distinct eigenvalues are linearly independent.
对应不同特征值的特征向量是线性无关的。
Eigenvalues and eigenvectors are fundamental concepts in linear algebra.
特征值和特征向量是线性代数中的基本概念。
The eigenvalues of a diagonal matrix are simply the diagonal entries.
对角矩阵的特征值就是对角线上的元素。
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