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## Main Question or Discussion Point

Let A_i (i=1,...,k) be a nonsingular complex matrix which size is M by M.

The question is how to find a complex matrix X which size is M by N such that:

span(A_1*X)=...=span(A_k*X)

(I guess that there must be relations between M,N and k when nontrival solution exists. )

ask:

1)if non trival solwhat's the condition for the existence of nontrival solutions?

2)Is there any method or related references for this question?

Thanks in advance:)

The question is how to find a complex matrix X which size is M by N such that:

span(A_1*X)=...=span(A_k*X)

(I guess that there must be relations between M,N and k when nontrival solution exists. )

ask:

1)if non trival solwhat's the condition for the existence of nontrival solutions?

2)Is there any method or related references for this question?

Thanks in advance:)