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Much is known about these Hadamard matrices, this talk by William Orrick gives a good overview:

The first few moments of the determinant ${\rm det}\,M$ are known exactly, for large $n$ the distribution of $|{\rm det}\,M|$ is conjectured to be log-normal.

For the number of singular matrices, see OEIS. The large-$n$ limit of the probability that a $n\times n$ matrix is singular is conjectured to be $n^2/2^n$.

Much is known about these Hadamard matrices, this talk by William Orrick gives a good overview:

The first few moments of the determinant $\det M$ are known exactly, for large $n$ the distribution of $|\det M|$ is conjectured to be log-normal.

For the number of singular matrices, see OEIS. The large-$n$ limit of the probability that a $n\times n$ matrix is singular is conjectured to be $n^2/2^n$.

Much is known about these Hadamard matrices, this talk by William Orrick gives a good overview:

The first few moments of the determinant ${\rm det}\,M$ are known exactly, for large $n$ the distribution of $|{\rm det}\,M|$ is conjectured to be log-normal.

For the number of singular matrices, see OEIS.

Much is known about these Hadamard matrices, this talk by William Orrick gives a good overview:

The first few moments of the determinant ${\rm det}\,M$ are known exactly, for large $n$ the distribution of $|{\rm det}\,M|$ is conjectured to be log-normal.

For the number of singular matrices, see OEIS. The large-$n$ limit of the probability that a $n\times n$ matrix is singular is conjectured to be $n^2/2^n$.

Much is known about these Hadamard matrices, this talk by William Orrick gives a good overview:

The first few moments of the determinant ${\rm det}\,M$ are known exactly, for large $n$ the distribution of $|{\rm det}\,M|$ is conjectured to be log-normal.

Much is known about these Hadamard matrices, this talk by William Orrick gives a good overview:

The first few moments of the determinant ${\rm det}\,M$ are known exactly, for large $n$ the distribution of $|{\rm det}\,M|$ is conjectured to be log-normal.

For the number of singular matrices, see OEIS.