Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with ...
SinceJk(λ)=(1λ00…001λ0…0⋮⋮⋮⋮⋱⋮0000…1): a) It is clear thatJk(λ).(11⋮1 )=(11⋮1);. b) Jk−Idn has rank n−1 and therefore the space ...
i.e., whose kth diagonal block, 1 ≤ k ≤ N is the Jordan block Jλk,mk and
with each element of the diagonal consisting of a single number lambda
block. For example, in the above form J, we have the eigenvalues λ = 1 with.
In order to understand this lecture, we should be familiar with the concepts introduced
Every n × n matrix A has a Jordan decomposition A = PJP-1. Proof: The
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If the matrix A has the Jordan form I, then there exists a nonsingular matrix T such that A ...
So a matrix may have n eigenvectors (if there are n J_i; the matrix is called
have signs attached to certain (real or purely imaginary) Jordan blocks in the