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- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_2562_Differential_Equations_with_Linear_Algebra/10%3A_Linear_Systems_of_Differential_Equations/10.05%3A_Constant_Coefficient_Homogeneous_Systems_IIIn this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has a...In this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has at least one eigenvalue of multiplicity r>1 such that the associated eigenspace has dimension less than r . In this case A is said to be defective. We will restrict our attention to some commonly occurring special cases.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/10%3A_Linear_Systems_of_Differential_Equations/10.05%3A_Constant_Coefficient_Homogeneous_Systems_IIIn this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has a...In this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has at least one eigenvalue of multiplicity r>1 such that the associated eigenspace has dimension less than r . In this case A is said to be defective. We will restrict our attention to some commonly occurring special cases.
- https://math.libretexts.org/Courses/Chabot_College/Math_4%3A_Differential_Equations_(Dinh)/08%3A_Linear_Systems_of_Differential_Equations/8.05%3A_Constant_Coefficient_Homogeneous_Systems_IIIn this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has a...In this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has at least one eigenvalue of multiplicity r>1 such that the associated eigenspace has dimension less than r . In this case A is said to be defective. We will restrict our attention to some commonly occurring special cases.
- https://math.libretexts.org/Courses/Red_Rocks_Community_College/MAT_2561_Differential_Equations_with_Engineering_Applications/09%3A_Linear_Systems_of_Differential_Equations/9.05%3A_Constant_Coefficient_Homogeneous_Systems_IIIn this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has a...In this section we consider the case where A has n real eigenvalues, but does not have n linearly independent eigenvectors. It is shown in linear algebra that this occurs if and only if A has at least one eigenvalue of multiplicity r>1 such that the associated eigenspace has dimension less than r . In this case A is said to be defective. We will restrict our attention to some commonly occurring special cases.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_420%3A_Differential_Equations_(Breitenbach)/10%3A_Linear_Systems_of_Differential_Equations/04%3A_Constant_Coefficient_Homogeneous_Systems_II\( \newcommand{\place}{\bigskip\hrule\bigskip\noindent} \newcommand{\threecol}[3]{\left[\boldsymbol{\begin{array}{r}#1\\#2\\#3\end{array}}\right]} \newcommand{\threecolj}[3]{\left[\begin{array}{r}#1\\[1\jot]#2\\[1...\( \newcommand{\place}{\bigskip\hrule\bigskip\noindent} \newcommand{\threecol}[3]{\left[\boldsymbol{\begin{array}{r}#1\\#2\\#3\end{array}}\right]} \newcommand{\threecolj}[3]{\left[\boldsymbol{\begin{array}{r}#1\\[1\jot]#2\\[1\jot]#3\end{array}}\right]} \newcommand{\lims}[2]{\,\bigg|_{#1}^{#2}} \newcommand{\twocol}[2]{\left[\boldsymbol{\begin{array}{l}#1\\#2\end{array}}\right]} \newcommand{\ctwocol}[2]{\left[\boldsymbol{\begin{array}{c}#1\\#2\end{array}}\right]} \newcommand{\cthreecol}[3]{\left[\boldsymbol{\begin{array}{c}#1\\#2\\#3\end{array}}\right]} \newco…