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Math Help - Linear Algebra

  1. #1
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    Linear Algebra

    If lambda max is the largest eigenvalue of a real symmetric matrix A, show that no diagonal entry of A can be larger than lambda max.
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  2. #2
    Super Member girdav's Avatar
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    Re: Linear Algebra

    We can show that \lambda_{\max}=\max_{\lVert x\rVert=1}x^tAx, using the fact that A is diagonalizable in an orthonormal base.
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  3. #3
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    Re: Linear Algebra

    can u please explain further in detail
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  4. #4
    Super Member girdav's Avatar
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    Re: Linear Algebra

    First, show the property about \lambda_{\max} I mentioned when A is a diagonal matrix. Jump to the general case using the fact that there exists an orthogonal matrix P and a diagonal matrix D such that P^tDP=A.
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