Category:Definitions/Characteristic Polynomials of Linear Operators
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This category contains definitions related to Characteristic Polynomials of Linear Operators.
Related results can be found in Category:Characteristic Polynomials of Linear Operators.
Definition 1
The characteristic polynomial of $\phi$ is the characteristic polynomial of the relative matrix of $\phi$ with respect to a basis of $M$.
Definition 2
Let $A \sqbrk x$ be the polynomial ring in one variable over $A$.
Let $I_M$ denote the identity mapping on $M$.
Let $M \otimes_A A \sqbrk x$ be the extension of scalars of $M$ to $A \sqbrk x$.
The characteristic polynomial of $\phi$ is the determinant of the linear operator $x I_M - \phi$ on $M \otimes_A A \sqbrk x$.
Pages in category "Definitions/Characteristic Polynomials of Linear Operators"
The following 3 pages are in this category, out of 3 total.