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Positive Definite Matrices — Gilbert Strang
Mathematics · positive-definite-matrices-tests-for-positive-definiteness
Problem Which of A 1 A_1 A 1 A 2 A_2 A 2 A 3 A_3 A 3 A 4 A_4 A 4 a > 0 a > 0 a > 0 a c > b 2 ac > b^2 a c > b 2 x x x x T A 1 x < 0 x^T A_1 x < 0 x T A 1 x < 0 A 1 = [ 5 6 6 7 ] A 2 = [ − 1 − 2 − 2 − 5 ] A 3 = [ 1 10 10 100 ] A 4 = [ 1 10 10 101 ] . A_1 = \begin{bmatrix} 5 & 6 \\ 6 & 7 \end{bmatrix} \quad A_2 = \begin{bmatrix} -1 & -2 \\ -2 & -5 \end{bmatrix} \quad A_3 = \begin{bmatrix} 1 & 10 \\ 10 & 100 \end{bmatrix} \quad A_4 = \begin{bmatrix} 1 & 10 \\ 10 & 101 \end{bmatrix}. A 1 = [ 5 6 6 7 ] A 2 = [ − 1 − 2 − 2 − 5 ] A 3 = [ 1 10 10 100 ] A 4 = [ 1 10 10 101 ] . Browse the problem library