S = {(2,5,3)} and T = {(2,0,5)} are two clusters. Two clusters that S and T...

S = {(2,5,3)} and T = {(2,0,5)} are two clusters. Two clusters that S and T spans are L(S) and L(T) . Is the intersection of L (S) and L (T) a vector space? If yes, find this vector space. If no, explain why there is no vector space.

Expert Solution

milcah answered 2 years ago

Given two sets S and T, the direct product of S and T is the set...

Given two sets S and T, the direct product of S and T is the set of ordered pairs S × T = {(s, t)|s ∈ S, t ∈ T}.Let V, W be two vector spaces over F. (a) Prove that V × W is a vector space over F under componentwise addition and scalar multiplication (i.e. if (v1, w1),(v2, w2) ∈ V × W, then (v1, w1) + (v2, w2) = (v1+w1, v2+w2) and a(v, w) = (av, aw)...

Compare and contrast the properties of open clusters and globular clusters. Indicate at least TWO way...

Compare and contrast the properties of open clusters and globular clusters. Indicate at least TWO way that they are similar? Indicate at least TWO way that they are different?

how do you figure out "s" and "t" for balanced polymorphism? pE=t/(s+t) qE=s/(s+t)

Show that Cp = T(∂S/∂T)p and Cv = T(∂S/∂T)V

Gaussian Mixture Model: the initial means and variances of two clusters in a GMM are as...

Gaussian Mixture Model: the initial means and variances of two clusters in a GMM are as follows: ?(1)=−3, ?(2)=2, ?21=?22=4. Let ?1=?2=0.5. Let ?(1)=0.2, ?(2)=−0.9, ?(3)=−1, ?(4)=1.2, ?(5)=1.8 be five points that need to cluster. Need to find 1) p(1|1) 2) p(1|2) 3) p(1|3) 4) p(1|4) 5) p(1|5)

Type or paste question here ax+by+c=0.ax+by+c=0. Let (s′,t′)(s′,t′) be the reflection of the point (s,t)(s,t) in...

Type or paste question here ax+by+c=0.ax+by+c=0. Let (s′,t′)(s′,t′) be the reflection of the point (s,t)(s,t) in ℓℓ. Find a formula that computes the coordinates of (s′,t′)(s′,t′) if one knows the numbers s,t,a,bs,t,a,b and cc. Your formula should depend on the variables s,t,a,bs,t,a,b and cc. It should work for arbitrary values of s,t,a,bs,t,a,b and cc as long as (a,b)≠(0,0)(a,b)≠(0,0). Its output should be a point.

assume that s and t are independent exponentially distributed, set u = min(s,t), v = max(s,t)....

assume that s and t are independent exponentially distributed, set u = min(s,t), v = max(s,t). prove that u and w = v-u are independent

Suppose S = {p, q, r, s, t, u} and A = {p, q, s, t}...

Suppose S = {p, q, r, s, t, u} and A = {p, q, s, t} and B = {r, s, t, u} are events. x p q r s t u p(x) 0.15 0.25 0.2 0.15 0.1 (a) Determine what must be p(s). (b) Find p(A), p(B) and p(A∩B). (c) Determine whether A and B are independent. Explain. (d) Arer A and B mutually exclusive? Explain. (e) Does this table represent a probability istribution of any random variable? Explain.

Calculate the average energy U(T) and entropy S(T) of a paramagnet with two energy states ±μH...

Calculate the average energy U(T) and entropy S(T) of a paramagnet with two energy states ±μH in the presence of magnetic field H. Take the limits of high and low temperature and draw schematically the U(T) and S(T) dependences for two different values of H.

Hierarchical clustering is sometimes used to generate K clusters, K > 1 by taking the clusters...

Hierarchical clustering is sometimes used to generate K clusters, K > 1 by taking the clusters at the K th level of the dendrogram. (Root is at level 1.) By looking at the clusters produced in this way, we can evaluate the behavior of hierarchical clustering on different types of data and clusters, and also compare hierarchical approaches to K-means. The following is a set of one-dimensional points: {6, 12, 18, 24, 30, 42, 48}. (a) For each of the...

Question