How to write an expression to represent z in terms of x_i and y_i?

Karsyn Stafford 2022-09-20 Answered
For two vectors z R d and a scalar y i R, and a symmetric matrix A , B , C R d × d , if we have
i = 1 n [ y i A B z C ] = 0
But how to write an expression to represent z in terms of x i and y i ? Something likez=?....
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Answers (1)

gerasseltd9
Answered 2022-09-21 Author has 6 answers
Let z = ( z 1 , , z d ), x i = ( x i 1 , , x i d ) and s = y i . Then
x i y i y i = y 1 s x 1 + + y n s x n = ( y 1 s x 1 1 , , y 1 s x 1 d ) + + ( y n s x n 1 , , y n s x n d ) ,
so
z j = y 1 s x 1 j + + y n s x n j = i y i s x i j = 1 s i y i x i j
where 1 j d
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