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let A = [ajk] be a n x n matrix
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consider the vector equation
Ax = tx where t is a number
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a value of t for which Ax = tx is satisfied is called
the Eigen value of the matrix A
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the corresponding solutions x are called Eigen
vectors of matrix A
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in matrix notation the above equation can also be written as
(A-tx)I=0
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By cramer's rule, the above equation has nontrivial solution if
and only if the determinant D(t) = 0
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by developing D(t), we get a nth degree equation in
t corresponding to A