All the eigenvalues of a symmetric matrix A are positive. Which of the following statements is FALSE? O The elements of the congruent matrix B are positive. O The elements of the congruent matrix B are greater than or equal to zero. The corresponding quadratic form is positive definite. O The determinant of A is postive.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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All the eigenvalues of a symmetric matrix A are positive. Which of the following statements is FALSE?
O The elements of the congruent matrix B are positive.
O The elements of the congruent matrix B are greater than or equal to zero.
The corresponding quadratic form is positive definite.
O The determinant of A is postive.
Transcribed Image Text:All the eigenvalues of a symmetric matrix A are positive. Which of the following statements is FALSE? O The elements of the congruent matrix B are positive. O The elements of the congruent matrix B are greater than or equal to zero. The corresponding quadratic form is positive definite. O The determinant of A is postive.
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