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Find a basis for the subspace of Mnxn consisting of all diagonal matrices.

Find a basis for the subspace of Mnxn consisting of all diagonal matrices.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Find a basis for the subspace of \( M_{n \times n} \) consisting of all diagonal matrices. **Explanation:** This problem requires identifying a set of diagonal matrices that forms a basis for the vector space of all \( n \times n \) diagonal matrices. Each matrix in the basis should have a single 1 on the diagonal and zeros elsewhere, representing the standard basis vectors for this subspace. The number of basis matrices will be \( n \), corresponding to the dimensions of the matrices.
Transcribed Image Text:**Problem Statement:** Find a basis for the subspace of \( M_{n \times n} \) consisting of all diagonal matrices. **Explanation:** This problem requires identifying a set of diagonal matrices that forms a basis for the vector space of all \( n \times n \) diagonal matrices. Each matrix in the basis should have a single 1 on the diagonal and zeros elsewhere, representing the standard basis vectors for this subspace. The number of basis matrices will be \( n \), corresponding to the dimensions of the matrices.
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