- #1
wasi-uz-zaman
- 89
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hi, please tell me what are the limitations for finding eigenvalues ?
thanks
thanks
Indubitably.WannabeNewton said:Could you be more specific? By the fundamental theorem of algebra, there always exists at least one (complex) solution to the characteristic polynomial so there will always be at least one (complex) eigenvalue, where complex means a number of the form ##a + bi##.
WannabeNewton said:Could you be more specific? By the fundamental theorem of algebra, there always exists at least one (complex) solution to the characteristic polynomial so there will always be at least one (complex) eigenvalue, where complex means a number of the form ##a + bi##.
Eigenvalues are a set of numbers associated with a square matrix that represent the scalar values of the matrix when multiplied by a corresponding eigenvector. They are often used in linear algebra to solve systems of equations.
Yes, Eigenvalues can be found for simultaneous equations. The Eigenvalues are the solutions to the characteristic equation of the coefficient matrix of the equations.
Eigenvalues provide a way to simplify and solve systems of equations by reducing them to smaller, more manageable equations. They can also help identify patterns and relationships between the equations.
No, it is not always possible to find Eigenvalues for simultaneous equations. In order to find Eigenvalues, the coefficient matrix of the equations must be square. If the matrix is not square, then it does not have Eigenvalues.
Eigenvalues can be used to solve any system of linear equations. However, they are most commonly used for homogeneous systems, where the right-hand side of the equations is equal to zero. For non-homogeneous systems, other methods may be more efficient.