MIT
18 06 -
Lecture 29
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Lecture 29 Positive de nite matrices All eigenvalues are positive All pivots are greater than zero All upper left determinants are greater than zero A has the form B B for some B with independent columns x A x 0 except x 0 Converting a matrix into a quadratic formula Finding eigenvalues and eigenvectors A has the form B B for some B with independent columns Restrictions B is square and symmetric Restrictions B is square and upper triangular When A is symmetric Restrictions B is rectangular Positive Semi De nite All eigenvalues are greater than or equal to zero All pivots are greater than or equal to zero All upper left determinants are greater than or equal to zero A has the form B B for some B with dependent columns x A x 0
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