Notes on fast matrix multiplcation and inversion
... Determining this sum requires n multiplications and n − 1 additions. Thus overall we get the product AB with mnp multiplications and m(n − 1)p additions. Note also that adding two n × m matrices requires nm additions, one for each of the nm position. In particular, multiplying two n×n matrices requi ...
... Determining this sum requires n multiplications and n − 1 additions. Thus overall we get the product AB with mnp multiplications and m(n − 1)p additions. Note also that adding two n × m matrices requires nm additions, one for each of the nm position. In particular, multiplying two n×n matrices requi ...
4.3 Determinants and Cramer`s Rule
... a1 x b1 y c1 a2 x b2 y c2 If the D 0, then the system has exactly one solution. The solution is: Dy Dx y x D D ...
... a1 x b1 y c1 a2 x b2 y c2 If the D 0, then the system has exactly one solution. The solution is: Dy Dx y x D D ...
Linear Algebra Refresher
... So supposed one of them (say y1-y2) is zero, Plug that into **, to get (x1-x2) (y2-y3) = 0, which means either x1-x2 is zero or y2-y3 is zero. In the former case, 2 points are in the same place, so clearly the 3 points are collinear. In the latter case, both lines are horizontal, so their slopes are ...
... So supposed one of them (say y1-y2) is zero, Plug that into **, to get (x1-x2) (y2-y3) = 0, which means either x1-x2 is zero or y2-y3 is zero. In the former case, 2 points are in the same place, so clearly the 3 points are collinear. In the latter case, both lines are horizontal, so their slopes are ...
Complex inner products
... 7 page 324). Note c) follows since the columns of S are orthogonal. If A is real we might need to choose a new S since the S we constructed in Theorem 3 might not be real, unless we chose it very carefully. For each eigenvalue λj of A, choose an orthonormal (real) basis Bj of the eigenspace correspo ...
... 7 page 324). Note c) follows since the columns of S are orthogonal. If A is real we might need to choose a new S since the S we constructed in Theorem 3 might not be real, unless we chose it very carefully. For each eigenvalue λj of A, choose an orthonormal (real) basis Bj of the eigenspace correspo ...
Sec 3.5
... Over the set of real number we have what we call the multiplicative inverse or reciprocal. The multiplicative inverse of a number is a second number that when multiplied by the first number yields the multiplicative identity 1. This is where the Identity Matrix comes in. Let A be a square matrix of ...
... Over the set of real number we have what we call the multiplicative inverse or reciprocal. The multiplicative inverse of a number is a second number that when multiplied by the first number yields the multiplicative identity 1. This is where the Identity Matrix comes in. Let A be a square matrix of ...
