Matrices and Markov chains
... The basic idea is that when probability of a certain event depends only on the immediately preceding observations, you can form a tree, or chain, to predict future probabilities. Notation: Recall that p(AjB) means the probability of an event A happening if you know the event B happened. For example, ...
... The basic idea is that when probability of a certain event depends only on the immediately preceding observations, you can form a tree, or chain, to predict future probabilities. Notation: Recall that p(AjB) means the probability of an event A happening if you know the event B happened. For example, ...
A recursive algorithm for computing Cramer-Rao
... upper left p X p submatrix of the n x n inverse Fisher information matrix F;’ provides the CR lower bound for these parameter estimates. Equivalently, the first p columns of F;’ provide this CR bound. The method of sequential partitioning [l] for computing the upper left p X p submatrix of F;’ and C ...
... upper left p X p submatrix of the n x n inverse Fisher information matrix F;’ provides the CR lower bound for these parameter estimates. Equivalently, the first p columns of F;’ provide this CR bound. The method of sequential partitioning [l] for computing the upper left p X p submatrix of F;’ and C ...
Theorems and counterexamples on structured
... This inequality was proven for n ≤ 3 by Varga (unpublished) as well as by Hershkowitz and Berman [24] and for n = 4 by Mehrmann [28]. In his survey paper [23], Hershkowitz posed the weaker conjecture that τ -matrices that are also GKK are stable. The above conjectures were plausible not only because ...
... This inequality was proven for n ≤ 3 by Varga (unpublished) as well as by Hershkowitz and Berman [24] and for n = 4 by Mehrmann [28]. In his survey paper [23], Hershkowitz posed the weaker conjecture that τ -matrices that are also GKK are stable. The above conjectures were plausible not only because ...
![λ1 [ v1 v2 ] and A [ w1 w2 ] = λ2](http://s1.studyres.com/store/data/020256186_1-44523acdcc73497aa300703df377fe57-300x300.png)
Homework 5
... (c) Use part (a) to show the equation of (b) simplifies to ~a · ~b = k~akk~bk cos θ (d) Use this to find the angle between the vector ~a = h1, 2i and ~b = h−2, 3i. (e) If k~ak = k~bk show that the two vector ~v = ~a + ~b and w ~ = ~a − ~b are orthogonal. Hint: Two vectors are orthogonal if and only ...
... (c) Use part (a) to show the equation of (b) simplifies to ~a · ~b = k~akk~bk cos θ (d) Use this to find the angle between the vector ~a = h1, 2i and ~b = h−2, 3i. (e) If k~ak = k~bk show that the two vector ~v = ~a + ~b and w ~ = ~a − ~b are orthogonal. Hint: Two vectors are orthogonal if and only ...
Diagonalisation
... equation Ax = λx is not of the standard form, since the right-hand side is not a fixed vector b, but depends explicitly on x. However, we can rewrite it in standard form. Note that λx = λIx, where I is, as usual, the identity matrix. So, the equation is equivalent to Ax = λIx, or Ax−λIx = 0, which i ...
... equation Ax = λx is not of the standard form, since the right-hand side is not a fixed vector b, but depends explicitly on x. However, we can rewrite it in standard form. Note that λx = λIx, where I is, as usual, the identity matrix. So, the equation is equivalent to Ax = λIx, or Ax−λIx = 0, which i ...