Question

Prove the AA similarity criterion!

Answer #1

Prove that if A is nonsingular, then AA^T is positive
deﬁnite.

Let A be a positive definite matrix. If a ∈ R, prove that aA is
positive definite if and only if a > 0.

Use the Divergence Criterion to prove that the sequence an =
(−1)n + 1 n diverges.

Use the Cauchy Criterion to prove the Bolzano–Weierstrass
Theorem, and find the point in the argument where the Archimedean
Property is implicitly required

Consider an initial population of 512 AA individuals 320 Aa
individuals , and 115 aa individuals aWhat are the frequencies of
the alleles ?

Describe how propinquity can perpetuate and increase perceived
similarity in our friendships. Describe how similarity can
perpetuate propinquity in our friendships.

a
population consists of 1000individuals with the following
genotypes:
AA 350
Aa 525
aa 125
what is the frequency of A?
frequency of a?
genotypic frequency of this population?
show calculations.

matrix A (nxn). Prove that the sum of the eigenvalues of a
matrix A equals to the sum of its diagonal elements (Aii) using the
similarity of transformation's notation.

Use the cosine similarity to measure similarity between
two users or between two items.
User-based collaborative filtering
Item-based collaborative filtering

A population has the following data:
Genotype Number
AA 65
Aa 5
aa 25
Calculate the allelic frequency for the
a allele.

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