Outline of the Pre-session Tianxi Wang
... When a solution exists, how many are the solutions? Is there an efficient algorithm that computes solutions? We will focus in systems that have a unique solution. For this, we need to impose enough structure on the problem: for n unknowns, we will need n linear independent equations. It is easy to d ...
... When a solution exists, how many are the solutions? Is there an efficient algorithm that computes solutions? We will focus in systems that have a unique solution. For this, we need to impose enough structure on the problem: for n unknowns, we will need n linear independent equations. It is easy to d ...
Homework #2
... 6. Let L : V 7→ V be a linear operator such that L2 = L (here L2 = L ◦ L). Such a mapping is said to be a projection operator. Show that: (a) ker(L) ∩ Ran(L) = {0} (b) if v ∈ V is given, then there are x ∈ ker(L), y ∈ Ran(L) such that v = x + y (c) V = ker(L) ⊕ Ran(L). 7. The first four Legendre pol ...
... 6. Let L : V 7→ V be a linear operator such that L2 = L (here L2 = L ◦ L). Such a mapping is said to be a projection operator. Show that: (a) ker(L) ∩ Ran(L) = {0} (b) if v ∈ V is given, then there are x ∈ ker(L), y ∈ Ran(L) such that v = x + y (c) V = ker(L) ⊕ Ran(L). 7. The first four Legendre pol ...
Exact differential A mathematical differential is said to be exact, as
... differentiations in the calculation of the second derivatives. So, in order for a differential dQ, that is a function of four variables to be an exact differential, there are six conditions to satisfy. In summary, when a differential dQ is exact: ...
... differentiations in the calculation of the second derivatives. So, in order for a differential dQ, that is a function of four variables to be an exact differential, there are six conditions to satisfy. In summary, when a differential dQ is exact: ...
