Help me how to find the base of the intersection of two subspaces

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Alfonzo S
Alfonzo S 2020-11-21
编辑： Matt J 2021-9-15
Hello, Can someone help me how to find the base of the intersection of two vector subspaces in matlab? please
Thanks!
Muchas gracias!

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Matt J
Matt J 2020-11-22
编辑：Matt J 2020-11-22
If the vectors form the columns of a matrix A and the vectors form the columns of a matrix B, then the basis of the intersecting space can be found as,
null( [null(A.').' ; null(B.').'] )
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Maria Christine Honecker
Maria Christine Honecker 2021-9-15
Hello, as I would like to use this further, I would be interested to know if there is any proof or source for this?
I am grateful for any answer.
Matt J
Matt J 2021-9-15
编辑：Matt J 2021-9-15
@Maria Christine Honecker You will find in many/most linear algebra texts that the row space and the null space of a matrix are orthogonal complements. Therefore, if a linear space is described by matrix equations E*x=0 then null(E) gives a basis for the subspace. Conversly, if B is a basis for the subpace, then E=null(B.').' is its equation coefficient matrix.
Therefore, the equation matrix for subspace L is null(A.').', the equation matrix for subspace M is null(B.').', and the equation matrix for their intersection is the concatenated system [null(A.').' ; null(B.').']. A basis for the concatenated system is null([null(A.').' ; null(B.').']).

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