The divergence of a higher order tensor field may be found by decomposing the tensor field into a sum of outer products, thereby allowing the use of the identity,
22.
This product of vectors \ scriptstyle a, \, b produces two terms : a scalar part from the inner product and a bivector part from the outer product.
23.
In abstract terms, the Euclid formula means that each primitive Pythagorean triple can be written as the outer product with itself of a spinor with integer entries, as in ( ).
24.
If the function to the left of the dot is " " " ( signifying null ) then the composite function is an outer product, otherwise it is an inner product.
25.
Even if the boldface dot were an outer product, that would make it a 3 \ times 3 matrix, which, in some sense, is even worse of a description!
26.
The antisymmetric part is the " exterior product " ( also called the " outer product " ) of the two vectors, the product of the contained exterior algebra:
27.
The inner product and outer product should not be confused with the interior product and exterior product, which are instead operations on vector fields and differential forms, or more generally on the exterior algebra.
28.
You find the mean, subtract it, then take the outer product of all of the vectors with themselves to get a 2x2 matrix, take the SVD of that matrix to find the slope of the line.
29.
If it's the notation that's confusing you, | \ psi _ i \ rangle \ langle \ psi _ i | is the outer product of the vector \ psi _ i with itself.
30.
T } } is the autocorrelation matrix, simply the outer product of inputs, is the function that diagonalizes a matrix, and is the function that sets all matrix elements on or above the diagonal equal to 0.
