Recent content by marxLynx

Proving case 3 is exactly the same as proving case 2, although we will be multiplying on the right instead of the left. Case 3: Let A be a singular matrix and let B be an invertible matrix, let AB be defined, and let (AB)-1 exist. We know that (AB)(AB)-1=I. As with case 2, we can write...

I find it amazing that there is even such a connection at all. In my mind, there's no reason that this should be so but it just is. I love math.

If A and B are square matrices and (AB)-1 exists, then A is invertible and B is invertible. Proof: If AB is defined and (AB)-1 exists, then there are four possibilities: A and B are both invertible, A is invertible and B is singular, A is singular and B is invertible, or A and B are both...

Consider this. If AB is defined and (AB)-1 exists, then there are only four possibilities. 1: A and B are both invertible. 2: A is invertible and B is singular. 3: A is singular and B is invertible. 4: A and B are both singular. Go through each case, and you'll see that A and B have to be...

Diagonalizing matrices can help computer run-times as well.

Euler is a name, and hence it is a proper noun. In this case, we do not say "an Euler" because Euler is a person. Saying "an --" implies that there are multiple cases, i.e. more than one Euler. However, if the name is attached to some mathematical object, then you can say "an Euler constant,"...

What are negative numbers? Have you even seen a negative number of chickens? i haven't. The idea is merely an abstraction of subtraction. An abstract idea doesn't have to have any physical significance at all, even if the idea was derived from physical things.

The only connection the region of integration has to the surface is that the region lies in the domain of the surface. The reason one would express a limit of x as a function of y is when one integrates a region that has a boundary that isn't constant at all its points (with respect to x). An...