Eigenvalues and eigenvectors are fundamental concepts in linear algebra, where an eigenvector of a matrix is a non-zero vector that changes by only a scalar factor when that matrix is applied to it, and the corresponding eigenvalue is that scalar. These concepts are crucial in understanding state-space models, as they help describe the dynamics of linear systems by simplifying the behavior of complex matrices into more manageable forms. They provide insight into the stability and response characteristics of systems modeled in state-space representation.
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