Linear Algebra : Diagonalizing Matrices
Not what you're looking for?
Let B be an nxn matrix with B^2 = B prove that B is diagonalizable, ie there exists an invertible matrix S so that S^-1 B S is diagonal. (Hint: all eigenvalues of B are either 0 or 1. For each k between 0 and n, consider the case when the nullity of B is k.)
Purchase this Solution
Solution Summary
Matrix diagonalization is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.
Solution Preview
Here we must consider some facts first and then get the answer step by step:
The minimal polynomial of a matrix A is the unique basis for the ideal of polynomials such that the matrix A vanishes on them.
According to the Cayley-Hamilton theorem if ...
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability