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question find a the maximum value of qx subject to the constraint x tx 1 b a unit vector u where this maximum is
question classify the quadratic then make a change of variable x py that transforms the quadratic form into one with
question find the matrix of the quadratic form assume x is in r3a 8x12 7x22 - 3x32 - 6x1x2 4x1x3 - 2x2x3b 4x1x2
question let a be the matrix of the quadratic form9x12 7x22 11x32 - 8x1x2 8x1x3it can be shown that the eigenvalues
question consider the problem of finding an eigenvalue of an n x n matrix a when an approximate eigenvector v is known
question let t rn rarr rn be a linear transformation that preserves lengths that is t x x for all x in rna show that
question a householder matrix or an elementary reflector has the form q i - 2uut where u is a unit vector show that q
question use the gram-schmidt process as in example to produce an orthogonal basis for the column space ofexample let v
question suppose a qr is a qr factorization of an m x n matrix a with linearly independent columns partition a as a1
question find a qr factorization of the matrix in exerciseexercise find an orthogonal basis for the column space of
question the columns of q were obtained by applying the gram-schmidt process to the columns of a find an upper
question find an orthonormal basis of the subspace spanned by the vectors in exerciseexercise the given set is a basis
question in parts a-d let u be the matrix formed by normalizing each column of the matrix a in exercisea compute utu
question determine which sets of vectors are orthonormal if a set is only orthogonal normalize the vectors to produce
question the matlab command roots p computes the roots of the polynomial equation p t 0 read a matlab manual and then
question use a matrix program to diagonalizeif possible use the eigenvalue command to create the diagonal matrix d if
question find a the largest eigenvalue andb the eigenvalue closest to zero in each case set x0 1 0 0 0 and carry out
question use the inverse power method to estimate the middle eigenvalue of the a in example with accuracy to four
question suppose is an eigenvalue of the b in exercise and that x is a corresponding eigenvector so that a - alphai-1x
question apply to a 3 x 3 matrix a whose eigenvalues are estimated to be 4 -4 and 3if the eigenvalues close to 4 and -4
question a common misconception is that if a has a strictly dominant eigenvalue then for any sufficiently large value