On Stabilizing Matrices by Simple Row Operations
ResearchPublished 1965
An affirmative answer is given to the following question: Let A be a nonsingular matrix. Are there matrices P and Q, each a product of diagonal and permutation matrices, such tha PAQ is stable; i.e., all of its eigenvalues have negative real part? This question arises in attempting to solve the equation Ax = b with an analog computer. The problem of finding a computationally practical method of doing what this Memorandum shows can be done remains open. An affirmative answer is given to the following question: Let A be a nonsingular matrix. Are there matrices P and Q, each a product of diagonal and permutation matrices, such that PAQ is stable; i.e., all of its eigenvalues have negative real part? This question arises in attempting to solve the equation Ax = b with an analog computer. The result is an existence theorem rather than an effective algorithm. The problem of finding a computationally practical method of doing what this Memorandum shows can be done remains open.
Document Details
- Copyright: RAND Corporation
- Availability: Available
- Year: 1965
- Print Format: Paperback
- Paperback Pages: 21
- Paperback Price: $20.00
- Document Number: RM-4698-PR
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Folkman, Jon H., On Stabilizing Matrices by Simple Row Operations, RAND Corporation, RM-4698-PR, 1965. As of October 10, 2024: https://www.rand.org/pubs/research_memoranda/RM4698.html
Folkman, Jon H., On Stabilizing Matrices by Simple Row Operations. Santa Monica, CA: RAND Corporation, 1965. https://www.rand.org/pubs/research_memoranda/RM4698.html. Also available in print form.
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