Null space

Mathematics

The nullspace of matrix A is the set of vectors x such that Ax=0. In other words, these vectors live in a space that A maps to zero, hence the name.

For example, if

A =
   1 0
   0 0

Then any vector x =
    0 a

where a can be any value, occupies the null space of A.

The nullspace is sometimes called the kernel.

A nullspace is the result of a copied   expression. If someone copies the space created by this expression, and pastes it, it looks like a normal space but it is in fact still a non-breaking space. So, unlike normal spaces in HTML, these do not get filtered out and as many spaces as are there are shown.

According to blaaf, nullspaces are actually two characters, one with hex code A0 and the other with 20. The 20 is the space, and the A0 is a nonsense character used to separate the spaces. Also, apparently using A0 alone works...

This is pretty useless. The only useful thing about it is that it works in the Chatterbox.......

The null space, or kernel, of a m x n matrix A is the set (vector space) of all solutions x to the equation Ax = 0 (including x = 0). The dimension of the null space is r - n, where r is the rank of A

If the null space of A is more than the set {0}, then the columns of A are dependent and A is not invertible. If the null space is {0} (and A is square), the columns are independent, and the matrix is surely invertible.