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Hi everyone,

I would need to get some help on the following question

Let A (m*n)

Let B (m*p)

Let L(A) be the span of the columns of A.

L(A) is orthogonal to L(B) <=> A'B=0

I suppose that the => direction is pretty obvious, since A is in L(A)

and B in is L(B).

Now I am not sure how to attack the <= statement. I guess that every

vector in L(A) is generated by the rows of A, and every vector in L(B)

is generated by the columns of B.

Therefore A'B=0, means Sum(i, j, constant_i*row_i of

A*constant_j*row_j of B).

How can I improve my argument?

I would need to get some help on the following question

Let A (m*n)

Let B (m*p)

Let L(A) be the span of the columns of A.

L(A) is orthogonal to L(B) <=> A'B=0

I suppose that the => direction is pretty obvious, since A is in L(A)

and B in is L(B).

Now I am not sure how to attack the <= statement. I guess that every

vector in L(A) is generated by the rows of A, and every vector in L(B)

is generated by the columns of B.

Therefore A'B=0, means Sum(i, j, constant_i*row_i of

A*constant_j*row_j of B).

How can I improve my argument?

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