6 A ug 2 00 3 Singular 0 / 1 - matrices , and the hyperplanes spanned by random 0 / 1 - vectors
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چکیده
Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =
منابع مشابه
1 6 A ug 2 00 4 Singular 0 / 1 - matrices , and the hyperplanes spanned by random 0 / 1 - vectors
Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =
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Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =
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تاریخ انتشار 2003