Given a matrix Y in R^(mxn). Find a transformation matrix Θ in R^(nxp) such that 1/m Θ^T Y^T YΘ=Ipxp, where Ipxp is identity matrix.

Colten Andrade 2022-09-21 Answered
Given a matrix Y R m × n . Find a transformation matrix Θ R n × p such that
1 m Θ T Y T Y Θ = I p × p ,
where 𝐼𝑝×𝑝 is identity matrix.
My attempt: 1 m Y Θ is orthogonal matrix and tried to find Θ satisfies it but that doesn't work.
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Answers (1)

Ashly Sanford
Answered 2022-09-22 Author has 9 answers
This can only work if Y has full rank. Now Θ could perform the basis transformation from the Gram-Schmidt procedure.
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