The matrix in Hessenberg form with the help of similarity transformation and the matrix in the similarity transformations.

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Nathalie Redfern · Accepted Answer

Matrix in Hessenberg form is H=[−7163893011],and the matrix in the similarity transformations is Q1=[1000100−41] Solution Given: The given matrix is [−7438−3332−1513] Approach: a) First check for a21≠0 b) If above condition is satisfied then take the matrix Q1 as Q1=[1000100−a31a211] c) Obtain Q1−1 with the help of Q1by changing the sign of the off- diagonal entries of Q1 d) Then write matrix in Hessenberg form like H=Q1⋅A⋅Q1−1 e) Write the matrix in the similarity transformations. Calculation: First check for a21≠0 in A=  a21≠0 in A=[−7438−3332−1513] As a21≠0, Write Q1 as Q1=[1000100−a31a211] Take value of a31,a21 from matrix A=a31,a21 from matrix A=[−7438−3332−1513] a21=8 a31=32 Write, Q1=[1000100−3281] After simplification it becomes, Q1=[1000100−41] Obtain Q1−1 with the help of Q1 by changing the sign of the off- diagonal entries of Q1. Put (4) in place of (−4) Q1−1=[100010041] Write matrix in Hessenberg form likeH=Q1⋅A⋅Q1−1. Put the values ofQ1,A0andQ1−1

The matrix in Hessenberg form with the help of similarity transformation and the

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