Question

what are the properties of characteristic vector and characteristic equation?

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Answer 1

Answer:

noun Mathematics.

a vector for which there exists a scalar such that the value of the vector under a given transformation is equal to the scalar times the vector.

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Answer 2

Answer:

Explanation:

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the characteristic equation in variable lambda is defined by

 det(A-lambdaI)=0,  

where I is the identity matrix and det(B) is the determinant of the matrix B. Writing A out explicitly gives

 A=[a_(11) a_(12) ... a_(1k); a_(21) a_(22) ... a_(2k); | | ... |; a_(k1) a_(k2) ... a_(kk)],   so the characteristic equation is given by

 |a_(11)-lambda a_(12) ... a_(1k); a_(21) a_(22)-lambda ... a_(2k); | | ... |; a_(k1) a_(k2) ... a_(kk)-lambda|=0  

The solutions lambda of the characteristic equation are called eigenvalues, and are extremely important in the analysis of many problems in mathematics and physics. The polynomial left-hand side of the characteristic equation is known as the characteristic polynomial.