Thanks! I can understand that O(n^(n-1)) = n^n. But can I say O(n^(n-1)) = n^(n-1)? I am trying to find a tighter asymptotic upper bound.
Similar to the second case.
Thanks!
Hi!
For the following functions, what are their big-O notation?
1. n^(n-1)
2. (n-1)^n
Should their big-O notations be the same as the original functions? i.e.
1. O(n^(n-1)) = n^(n-1)?
2. O((n-1)^n) = (n-1)^n?
Please help!
Many thanks!
What if we only consider A is positive definite? Then B is positive definite and C should be positive definite too.
Can we compute the inverse of C directly from A in this case?
Thank you!
Suppose A is a invertible n-by-n matrix. Let B be the inverse of A, i.e. B = A^(-1).It is trivial that A = B^(-1).
If we construct a matrix C whose entry is the square of corresponding entry of B, i.e. C_ij = (B_ij)^2, then we compute the inverse of C.
We can compute the inverse of C...
For semidefinite programming (SDP), we have the primal and dual forms as:
primal
min <C,X>
s.t. <A_i,X> = b_i, i=1,...,m
X>=0
dual
max <b,y>
s.t. y_1*A_1 + ... + y_m*A_m <=C
where the data A_i and C are assumed to be real symmetric matrices in many textbooks and online...
Consider two matrices:
1) A is a n-by-n Hermitian matrix with real eigenvalues a_1, a_2, ..., a_n;
2) B is a n-by-n diagonal matrix with real eigenvalues b_1, b_2, ..., b_n.
If we form a new matrix C = A + B, can we say anything about the eigenvalues of C (c_1, ..., c_n) from the...
Consider a and u are vector of n entries,
why the supremum of a dot u subject to the 2-norm of u is less than or equal to r equals r times 2-norm of a, i.e. sup{a.u | ||u||_2 <=r} = r ||a||_2?
How can I work out that?
Thank you!
Is it possible to express a n-by-n positive semi-definite matrix (A) in terms of a sum of n terms of something, i.e. A = B1+B2+...+Bn, where each Bi has similar structure?
Thanks!