[SciPy-user] howto construct matrix A: dot(A.T, A) is positive-definite

Gael Varoquaux gael.varoquaux@normalesup....
Fri Oct 5 12:14:52 CDT 2007


On Fri, Oct 05, 2007 at 12:58:54PM -0400, Dominique Orban wrote:
> > No, this is not correct. dot() is simply matrix multiplication.

> Isn't this counter-intuitive, given that for vectors, dot(u,v) is u^T v ?

That's why, when you do linear algebra, you write u^t v for the scalar
product of two vectors. In a curved space of metric G (G is a square
matrix of dimension the dimension of the space), you write the scalar
product u.v = u^t G v, ... And so on, and so forth. You cannot
interchange scalar product and matrix multiplication.

Gaël


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