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In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive-definite. See, in particular: Positive-definite bilinear form; Positive-definite function; Positive-definite function on a group; Positive-definite functional; Positive-definite kernel
Positive-definiteness arises naturally in the theory of the Fourier transform; it can be seen directly that to be positive-definite it is sufficient for f to be the Fourier transform of a function g on the real line with g(y) ≥ 0.
In mathematics, Sylvester’s criterion is a necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite. Sylvester's criterion states that a n × n Hermitian matrix M is positive-definite if and only if all the following matrices have a positive determinant: the upper left 1-by-1 corner of M,
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This makes a positive definite matrix. More properties of controllable systems can be found in Chen (1999 , p. 145 ), as well as the proof for the other equivalent statements of “The pair ( A , B ) {\displaystyle ({\boldsymbol {A}},{\boldsymbol {B}})} is controllable” presented in section Controllability in LTI Systems.
A Riemannian metric is a metric with a positive definite signature (v, 0). A Lorentzian metric is a metric with signature ( p , 1) , or (1, p ) . There is another notion of signature of a nondegenerate metric tensor given by a single number s defined as ( v − p ) , where v and p are as above, which is equivalent to the above definition when ...
Jenna Bush Hager/TODAY When fans saw that Jenna released the Hager family holiday card on the air, they rushed to the comments to share how adorable it was. "This is awesome!"
In the 8 a.m. ET hour, the “Today” anchors aired a special goodbye package to Kotb that began with Guthrie giving a pre-taped interview from the makeup room where the two co-anchors spent ...