Give dim H and the E-coordinate map.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%

need help with matrix algebra

a) Give \(\dim H\) and the \(\mathcal{E}\)-coordinate map.
Transcribed Image Text:a) Give \(\dim H\) and the \(\mathcal{E}\)-coordinate map.
Given the subspace 

\[ H = \left\{ \begin{bmatrix} a & 0 \\ b & c \end{bmatrix} \ \middle| \ a, b, c \in \mathbb{R} \right\}. \]

Thus, \( H \) is the space of lower triangular \( 2 \times 2 \)-matrices. The set

\[ \mathcal{E} = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix} \right\} \]

is a basis of \( H \).
Transcribed Image Text:Given the subspace \[ H = \left\{ \begin{bmatrix} a & 0 \\ b & c \end{bmatrix} \ \middle| \ a, b, c \in \mathbb{R} \right\}. \] Thus, \( H \) is the space of lower triangular \( 2 \times 2 \)-matrices. The set \[ \mathcal{E} = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix} \right\} \] is a basis of \( H \).
Expert Solution
steps

Step by step

Solved in 3 steps with 15 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,