Archives for Mathematical Physics
Examples of Hilbert Spaces
Hilbert Spaces can be FINITE dimensional or INFINITE Dimensional Finite Dimensional Hilbert Spaces n-Tuples of real numbers - $R^n$ - $R^5$ Inner Product would be just the dot product of…
Subspaces of Vector Spaces, Invariant Subspaces
The idea is to create a RESTRICTED space within the given vector space. Within R3 $\R^3$: $\{ \vec{i}, \vec{j}, \vec{k} \}$ we can define a space that is far more…
How to think of complex numbers
Think of it as a duo - there's actually TWO (real) numbers wrapped up in a single complex number. Think of it as a regular vector , but with a…
Vector Spaces Examples
The set of functions that take in a natural number n and return a REAL number. \ Functions of ONE Real Variable ( REAL to REAL) \ Of what use…
The nowhere continuous function
For example, the nowhere continuous function \