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achuthan1988
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Q)Different eigenvectors corresponding to an eigenvalue of a matrix must be linearly dependant?
Is the above statement true or false.Give reasons.
Is the above statement true or false.Give reasons.
achuthan1988 said:Q)Different eigenvectors corresponding to an eigenvalue of a matrix must be linearly dependant?
Is the above statement true or false.Give reasons.
An eigenvalue is a scalar that represents the magnitude of the change in a vector when multiplied by a matrix. An eigenvector is a vector that does not change direction when multiplied by a matrix and is associated with a specific eigenvalue.
The true or false eigenvalue problem is a mathematical problem that involves determining if a given matrix has any real eigenvalues. This problem is also known as the spectral theorem.
The true or false eigenvalue problem is solved by finding the characteristic polynomial of the given matrix and then solving for the roots of the polynomial. If all of the roots are real, then the matrix has real eigenvalues. If any of the roots are complex, then the matrix does not have real eigenvalues.
The true or false eigenvalue problem is important in many areas of mathematics and science, as it allows us to understand the behavior and properties of matrices. It is also used in various applications such as image processing, data compression, and quantum mechanics.
The true or false eigenvalue problem is closely related to diagonalization, as a matrix can only be diagonalized if it has a full set of eigenvectors. Diagonalization is the process of finding a diagonal matrix that is similar to the given matrix and can simplify many calculations involving the matrix.