Illustrate that for any vector dot is greater than zero
Consider A be a real, symmetric 3x3 matrix with distinct, positive eigenvalues lambda1, lambda2, and lambda3. Consider b1, b2, and b3 be respective eigenvectors. Illustrate that for any vector in R3, v dot (Av) is greater than or equal to zero.
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Assume v is eigenvector of A related with eigenvalue lambda and is also the eigenvector of B related with eigenvalue upsilon. Illustrate that lambda + upsilon is eigenvalue of A + B.
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Consider b1, b2, and b3 be respective eigenvectors. Illustrate that for any vector in R3, v dot (Av) is greater than or equal to zero.
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