ng answer will be fined worth a correct answer. If a real matrix A satisfies A" - - A then it is diagonalizable by a unitary matrix. If A is diagonalizable then all of its eigenvalues must be distinct (ie. each eigenvalue has multiplicity 1). IH A and B represent same linear transformation T : R" -→ R" then they have the same rank. If A is singular then its exponential e is also singular. Consider an LDU decomposition of a square matrix A. The product of the diagonal entries of the diagonal matrix D is the determinant of A.
ng answer will be fined worth a correct answer. If a real matrix A satisfies A" - - A then it is diagonalizable by a unitary matrix. If A is diagonalizable then all of its eigenvalues must be distinct (ie. each eigenvalue has multiplicity 1). IH A and B represent same linear transformation T : R" -→ R" then they have the same rank. If A is singular then its exponential e is also singular. Consider an LDU decomposition of a square matrix A. The product of the diagonal entries of the diagonal matrix D is the determinant of A.
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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Transcribed Image Text:Determine whether the following statements are true or false.
Here a wrong answer will be fined worth a correct answer.
* Iif a real matrix A satisfies A" = -A then it is diagonalizable by a unitary matrix.
* If A is diagonalizable then all of its eigenvalues must be distinct (ie. each eigenvalue has multiplicity 1).
: If A and Brepresent same linear transformation T : R" -→ R* then they have the same rank.
• If A is singular then its exponential e is also singular.
* Consider an LDU decomposition of a square matrix A. The product of the diagonal entries of the diagonal matrix D is the determinant of A.
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