You have a data matrix X = Rnxd where each row corresponds to a student and each column corresponds to their grade on an assignment. The final column is their cumulative grade. All grades are numerical values. Give an upper bound on the rank of this matrix. Do you think it is well approximated by an even lower rank matrix? Why or why not?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.7: Applications
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1.
You have a data matrix X = Rnxd where each row corresponds to a student
and each column corresponds to their grade on an assignment. The final column is their
cumulative grade. All grades are numerical values. Give an upper bound on the rank of this
matrix. Do you think it is well approximated by an even lower rank matrix? Why or why
not?
Transcribed Image Text:1. You have a data matrix X = Rnxd where each row corresponds to a student and each column corresponds to their grade on an assignment. The final column is their cumulative grade. All grades are numerical values. Give an upper bound on the rank of this matrix. Do you think it is well approximated by an even lower rank matrix? Why or why not?
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