Can I simplify the following vector?Let a and b be n × 1 vectors and...

Kade Reese

Kade Reese

Answered

2022-07-20

Can I simplify the following vector?
Let a and b be n × 1 vectors and M 1 , M 2 , . . . , M n be n × n matrices.
Is there a way to write the following vector:
v = [ a T M 1 b a T M 2 b a T M n b ]
in such a way that reads v = a T M n e w b, where M n e w is just a manipulation of the M i matrices?
I know I can do:
v = [ a T M 1 a T M 2 a T M n ] b
But then I cannot get the vector a "out of the brackets".

Answer & Explanation

sviudes7w

sviudes7w

Expert

2022-07-21Added 12 answers

You could write
v = ( a T a T ) ( M 1 M n ) b .
If you like, you could write the matrix on the left compactly using the fact that
( a T a T ) = a T I ,
where I denotes a size n identity matrix and ⊗ denotes the Kronecker product.

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