Jordan canonical form of matrix

Reference no: EM13124341

For the given 4x4 matrix, find P such that INV(P)AP is in Jordan Canonical Form.

A = | 2 1 0 0 |
| -1 4 0 0 |
| 0 0 2 1 |
| 0 0 -1 2 |

It is easy to find repeated eigenvalues (3, 2+i, 2-i).

If I treat the upper block as a 2x2 matrix, I can find P = [1 0; 1 1] (Note: Using Matlab notation here). This correctly results in INV(P)AP = [3 1; 0 3] which is in the form needed.

I am not clear what to do with the complex eigenvalues, and I am not sure how to view the entire matrix. By that I mean, I am not confident that examining the matrix as a smaller (2x2) block is heading me in the right direction.

Reference no: EM13124341

Questions Cloud

Preparing an income statement : Prepare an income statement through gross profit for the year ended December 31, 2004.

How will the character of the income or loss be determined : The character of any income or loss will be ordinary if the contributed property is sold by the partnership within five years after the date of contribution regardless of the character of the asset in the hands of the partnership.

Uniform continuity and boundedness : Let f:R->R be uniformly continuous on R (the reals) and let f_n(x)=f(x+1/n) for x in the reals. Show that (f_n) converges uniformly on the reals to f.

Why does a business need to understand elasticity of demand : Why does a business need to understand elasticity of demand and calculate the elasticity of demand between prices $6 to $8

Jordan canonical form of matrix : If I treat the upper block as a 2x2 matrix, I can find P = [1 0; 1 1] (Note: Using Matlab notation here). This correctly results in INV(P)AP = [3 1; 0 3] which is in the form needed.

Straight-line method of depreciation : A change from the straight-line method of depreciation to an accelerated method should be accounted for as a(n)

Define youth as a consecutive of challenging : define Youth as a consecutive of challenging

How is the auditors assessment of control risk affected : How is the auditor's assessment of control risk affected if a documented control procedure is not operating effectively? Explain the effect of such an assessment on the nature of audit tests of account balances.

Description of fermat little theorem : Please DO NOT USE Euler's function. You can only use Fermat's Little theorem if needed.

User Account

All Pages