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okay in this lesson im going to talk about the orthogonal decomposition theorem okay so lets suppose that we have a subspace here okay of r n okay so that is representing this figure by a plane okay then each for each y belonging to rn belong to a vector space okay this can be written uniquely in the form of y hat okay which is the projection onto the subspace of rnw plus the orthogonal vector or in this case this is z okay z is acting as the orthogonal complement of w okay all right so this is so to do this is just an extension on the previous video where i was so where we did the uh projection of a vector onto another vector okay all right so were going to so we can find y okay so y hat can be constructed by using the same idea okay from the previous lesson okay so okay y hat okay we can construct y hat by writing it as okay so its going to be y the vector y dotted with u lets say u1 okay times u1 okay okay so u1 is belongs belongs to the span of w okay so were going to have a