搜搜做题作业网求解下线性代数特征值的问题
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求解下线性代数特征值的问题
M is a symmetric real 2x2 matrix.It has two eigenvalues,\x150 and \x151.
• If both eigenvalues are positive,show that,for any 2D vector x,0 \x14 xTMx \x14 (max(\x150,\x151))xT x.
• If one eigenvalue is zero,show that there is some vector x 6= 0 such that Mx = 0.
• If one eigenvalue is positive and one is negative,show that there is some vector x 6= 0 such
that xTMx = 0
• A matrix M is positive definite if,for any vector x,xTMx > 0.Assume that M is
symmetric,real,and positive definite.What can you say about its eigenvalues?
M is a symmetric real 2x2 matrix.It has two eigenvalues,\x150 and \x151.
• If both eigenvalues are positive,show that,for any 2D vector x,0 \x14 xTMx \x14 (max(\x150,\x151))xT x.
• If one eigenvalue is zero,show that there is some vector x 6= 0 such that Mx = 0.
• If one eigenvalue is positive and one is negative,show that there is some vector x 6= 0 such
that xTMx = 0
• A matrix M is positive definite if,for any vector x,xTMx > 0.Assume that M is
symmetric,real,and positive definite.What can you say about its eigenvalues?
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