Let A be a matrix with an eigenvalue λ that has an algebraic
multiplicity of k,...
Let A be a matrix with an eigenvalue λ that has an algebraic
multiplicity of k, but a geometric multiplicity of p < k, i.e.
there are p linearly independent generalised eigenvectors of rank 1
associated with the eigenvalue λ, equivalently, the eigenspace of λ
has a dimension of p. Show that the generalised eigenspace of rank
2 has at most dimension 2p.
Explain the distinction between algebraic multiplicity
and geometric multiplicity of a matrix. Justify your
answer (explain)...
Explain the distinction between algebraic multiplicity
and geometric multiplicity of a matrix. Justify your
answer (explain)
These questions follow the exercises in Chapter 4 of the book,
Scientic Computing: An Introduction, by Michael Heath. They study
some of the properties of eigenvalues, eigenvectors, and some ways
to compute them.
True/False? If 0 is an eigenvalue of a 3x3 matrix A with
geometric multiplicity ug(A,0)=3, then...
True/False? If 0 is an eigenvalue of a 3x3 matrix A with
geometric multiplicity ug(A,0)=3, then A is the zero-matrix, that
is A=0
The answer is True, but I don't understand why.
Find the geometric means in the following
sequence.
-14, ?, ?, ?, ?, -235,298
A. 98,...
Find the geometric means in the following
sequence.
-14, ?, ?, ?, ?, -235,298
A. 98, 686, 4,802, 33,614
B. -1,960, -2,940, -3,920, -4,900
C. -98. -686, -4,802, -33,614
D. -686, -4,802, -33,614.-235,313
Kindly explain well