Recent content by Sue_2010

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    Basis and Subspace Help: Exploring the Relationship between Vectors e and d

    Hello everyone, I really want to get some feedback. Thank you!
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    Basis and Subspace Help: Exploring the Relationship between Vectors e and d

    And how do you get D in null(E') and E in null(D') ?
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    Basis and Subspace Help: Exploring the Relationship between Vectors e and d

    Hi rochfor1, Now I understand that it's not right to compare null(D) and row(E), since they are of different dimensions. Can we compare the projections to null(D) and row(E) in terms of their effects to the separability of the pairs of vectors, (c11 , c12) ... (cn1 , cn2) I mentioned in...
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    Basis and Subspace Help: Exploring the Relationship between Vectors e and d

    Thank you for your reply! You are right, E and D are matrices. Let me state my question more clearly. I want to find a projection that maximally preserves the Euclidean distance between two points (vectors in general). Consider a 2-D example as show in the figure. The direction that maximally...
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    Basis and Subspace Help: Exploring the Relationship between Vectors e and d

    Suppose I have 3 vectors e1, e2, e3 that spans the subspace E, another 3 vectors d1, d2, d3 that spans the subspace D. If I also know that e1’d1 = 0, e2’d2 = 0, e3’d3 = 0, are there any conclusions I can make in terms of E and D? like row(E) = null(D)?
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    Can the null space of matrix B be used for data projection?

    about null space projection Homework Statement If I have a collection of data points (vectors), and x and y are two vectors among them. I want to project the data to a direction that the Euclidean distance between x and y is Maximally preserved. Then this direction should be the row space of...
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    Can the null space of matrix B be used for data projection?

    Hello everyone, If I have a collection of data points (vectors), and x and y are two vectors among them. I want to project the data to a direction that the Euclidean distance between x and y is Maximally preserved. Then this direction should be the row space of (x-y)’, denoted as row( (x-y)’...
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