Adv.
How many rotations are required to reduce each of above matrices to tridiagonal form.
[21.41441.41461.41411.4142]
How the Householder method is better than Given’s method?
Using Householder’s transformation, reduce the following matrices in tridiagonal form and find all the eigen values and eigen vectors. Write the strum sequence.
[122212221]
[1√2√22√2−√2−1√2√2−1√2√22√2√2−3]
If the orthogonal transform is of the form p=1−2WWT where W is a column vector such that WTW=1. Prove that P is symmetric and orthogonal.
Write the strum sequence and find the eigen values of following matrix:
[1−1000011−1000011−1000011−1000011−1000011]
Use LR and QR both the methods to find the eigen values of the following matrix:
A=[3214]
Let R be a ring in which a2=a,∀a∈R (such a ring is called a Boolean ring). Show that 2a=0,∀a∈R , and R is commutative. Further show that the only Boolean ring that is an integral domain is Z2.
Let R be a ring and a,b∈Rsuch that ab=ba . Prove that for any positive integer (a+b)n=an+(n1)an−1b+⋯+(nn−1)abn−1+bn .
Let d be any integer. Prove that Z[√d]={a+b√d|a.b∈Z} is an integral domain and Z[√d]={a+b√d|a.b∈Z} is a field.
All Questions
Physics
Chemistry
Mathematics
English
Organic Chemistry
Inorganic Chemistry
Physical Chemistry
Algebra
Geometry