Purchase Solution

Real Matrix with Upper Triangular Block Structure

Not what you're looking for?

Ask Custom Question

** Please see the attached file for the complete problem statement **

Let A be a real matrix having the upper triangular block structure

A_11 A_12 A_13 ... A_1n

0 A_22 A_23 ... A_2n

0 0 A_33 ... A_3n

. . . .
. . . .
. . . .

0 0 0 ... A_nn

where, for all i, j with 1 <= i <= n and 1 <= j <= n, block A_ij is a 2 x 2 matrix; thus A is a 2n x 2n matrix.

(a) Prove that det(A) = det(A_11) * det(A_22) * det(A_33) * ... * det(A_nn).

This is where I need help. I need to know how to write up the proof of this expansion rigorously, but in a reasonable amount of time and space.

(b) Give a simple procedure for computing the eigenvalues of A, including proof.

Attachments
Purchase this Solution

Solution Summary

This solution provides a detailed, step-by-step proof for parts (a) and (b), with a full explanation at each step.

Solution provided by:
Education
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
Recent Feedback
  • "Thanks for your assistance. "
  • "Thank you. I understand now."
  • "Super - Thank You"
  • "Very clear. I appreciate your help. Thank you."
  • "Great. thank you so much!"
Purchase this Solution


Free BrainMass Quizzes
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

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.