 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof-resit/5/a/solution

λ

is an eigenvalue of an

n \times n

P

if there is a nonzero vector

v

such that

P v = λ v, v \neq = 0 .

Any such vector is an eigenvector corresponding to

λ

. The requirement that an eigenvector be nonzero is essential: the zero vector would satisfy the equation for every scalar and would convey no information.

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