Let A,B be two matrices with linearly independent columns . If Col(A)=Col(B) then A(A^TA)^{-1}A^T=B(B^TB)^{-1}B^T True or False?

Albarellak 2021-02-21 Answered
Let A,B be two matrices with linearly independent columns . If Col(A)=Col(B) then A(ATA)1AT=B(BTB)1BT
True or False?
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Expert Answer

funblogC
Answered 2021-02-22 Author has 91 answers

Step 1
Let A and B are two matrices.
And A and B are linearly independent columns.
Step 2
If col(A) =col(B)
Since A and B are linearly independent.
So αA+βB=0
So, the matrices are orthonormal,
So AAT=BBT
From this,
(AAT)1=(BBT)1
Then,
A(ATA)1AT=B(BTB)1BT
Since in matrices,
AAT=≠ATA
So the answer is false.
The correct option is (2).

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Jeffrey Jordon
Answered 2022-01-23 Author has 2064 answers

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