Linear Algebra 6.4 Symmetric Matrices Set 6.4 Pdf

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One of the beauties of linear algebra is the variety of matrices-- orthogonal matrices, symmetric matrices. We'll see more and more kinds of matrices. And sometimes they're named after somebody who understood that they were important and found their special properties. So a Markov matrix is a matrix with the columns adding up to 1 and no negative numbers involved, no negative numbers. …

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More interesting (and useful), is the ability to use a 2-variable function (or lambda) to create a matrix. Here we create an indicator function which is 1 on the diagonal and then use it …

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One of the beauties of linear algebra is the variety of matrices-- orthogonal matrices, symmetric matrices. We'll see more and more kinds of matrices. And sometimes they're named after somebody who understood that they were important and found their special properties. So a Markov matrix is a matrix with the columns adding up to 1 and no negative numbers involved, no negative numbers. …

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This chapter enters a new part of linear algebra. The first par t was about Ax = b: matrices and (most important) symmetric matrices. All have special λ’s and x’s: 1. Markov matrix: Each column of P adds to 1, so λ = 1 is an eigenvalue. 2. P is singular, so λ = 0 is an eigenvalue. 3. P is symmetric, so its eigenvectors (1,1) and (1,−1) are perpendicular. The only eigenvalues of a

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Real symmetric 3×3 matrices have 6 independent entries (3 diagonal elements and 3 off-diagonal elements) and they have 3 real eigenvalues (λ₀ , λ₁ , λ₂).

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