Applying transformations in succession Suppose that A and B are 2

... Now, this determinant is zero exactly when λ = 1 or 2, so these are the eigenvalues of A. ...

... Now, this determinant is zero exactly when λ = 1 or 2, so these are the eigenvalues of A. ...

Some Matrix Applications

... This page is a brief introduction to two applications of matrices - the solution of multiple equations, and eigenvalue/eigenvector problems (don't worry if you haven't heard of the latter). Before reading this you should feel comfortable with basic matrix operations. If you are confident in your abi ...

... This page is a brief introduction to two applications of matrices - the solution of multiple equations, and eigenvalue/eigenvector problems (don't worry if you haven't heard of the latter). Before reading this you should feel comfortable with basic matrix operations. If you are confident in your abi ...

Defn: A set V together with two operations, called addition and

... Defn: A set V together with two operations, called addition and scalar multiplication is a vector space if the following vector space axioms are satisfied for all vectors u, v, and w in V and all scalars, c, d in R. Vector space axioms: a.) u + v is in V b.) cu is in V c.) u + v = v + u d.) (u + v) ...

... Defn: A set V together with two operations, called addition and scalar multiplication is a vector space if the following vector space axioms are satisfied for all vectors u, v, and w in V and all scalars, c, d in R. Vector space axioms: a.) u + v is in V b.) cu is in V c.) u + v = v + u d.) (u + v) ...

Let v denote a column vector of the nilpotent matrix Pi(A)(A − λ iI)ni

... where ni is the so called nilpotency. Theorem 3 in [1] shows that APi (A)(A − λi I)ni −1 = λi Pi (A)(A − λi I)ni −1 . which means a column vector v of the matrix is an eigenvector corresponding to the eigenvalue λi . The symbols are explained in [1]. However it is worth noting that Pi (A)(A − λi I). ...

... where ni is the so called nilpotency. Theorem 3 in [1] shows that APi (A)(A − λi I)ni −1 = λi Pi (A)(A − λi I)ni −1 . which means a column vector v of the matrix is an eigenvector corresponding to the eigenvalue λi . The symbols are explained in [1]. However it is worth noting that Pi (A)(A − λi I). ...

Exam 3

... Problem 2: (15 points) True/False. If the statement is always true, mark true. Otherwise, mark false. You do not need to show your work. (Any work will not be graded.) (a) There exists a real 2 × 2 matrix, A, with eigenvalues λ1 = 1, λ2 = i. (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 fo ...

... Problem 2: (15 points) True/False. If the statement is always true, mark true. Otherwise, mark false. You do not need to show your work. (Any work will not be graded.) (a) There exists a real 2 × 2 matrix, A, with eigenvalues λ1 = 1, λ2 = i. (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 fo ...