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Reflections 21.8 Reflect on your understanding
In addition to the reflection activities below, re-read
Section 21.2 Terminology and notation . Be sure you understand each of the new definitions introduced in this chapter, and spend some time committing them to memory.
1. Calculation procedure for eigenvalues.
Summarize the algebra and reasoning that led from the definition
\(A \uvec{x} = \lambda \uvec{x}\) of
eigenvector and
eigenvalue to the
characteristic equation \(\det (\lambda I - A) = 0 \) used to calculate eigenvalues.
2. Calculation procedure for eigenvectors.
What is the earliest point in
Procedure 21.4.4 , applied to a specific eigenvalue of a matrix, at which you will know the dimension of the corresponding eigenspace?
3. Singular matrices versus eigenvalue zero.
Explain the reasoning/theory behind the connection between a matrix being
singular and having eigenvalue
\(0\text{.}\)
