Lec01.pdf Matrices, linear transforms, linear systems

Corrections:

1. 1)Slide 15 Cramer’s rule refers to a way to use the determinant to solve a system of equations rather than to a way to compute the determinant. 
   

2. 2)Slide 17: If a matrix A is full rank the eigenvalues are non-zero and if they are distinct there are at least n independent eigenvectors (not necessarily orthogonal), where n=rank(A).
   

Lec02.pdf Vector spaces, orthogonal basis

Corrections:

1. 1)Slide 5-6 typo: the sum is written explicitly, remove the sigma notation
   

2. 2)Slide 5 and 7 write b^T a to be consistent with the complex notation in Slide 6. Note: the result is the same
   

Lec03.pdf Example problems

Corrections:

1. 1)Slide 12 the determinant is a polynomial of degree 3, not 2
   

Lec04.pdf Eigenbases

Lec05.pdf Quadratic forms and signal space

Corrections:

1. 1)In the figure (a) on slide 10 you also assume sigma_x = sigma_y to obtain circles.
   

Lec06.pdf Signal space

Lec08.pdf ODE solutions as a system of equations

Corrections: Correction_Eq6.pdf

Lec09.pdf ODE solutions and examples

Lec10.pdf Probabilty 1.

Corrections: In slide 22 it is stated that any linear combination of Gaussian random variables is always a Gaussian. This is indeed true for independent variables. If variables are not independent they need to be jointly Gaussian in order for their linear combination to be a Gaussian.  

Lec11.pdf Probabilty 2.

Corrections: In the plot in slide 5 it is also assumed that sigma_x=sigma_y

Lec12.pdf Probability 3

Lec13.pdf Probability Central Limit Theorem.

Corrections: In slide 2 the statement of the CLT has a typo. In the equation you need to subtract <x_i> rather than <x> and the result will have zero mean and variance sigma^2. A more precise statement for independent but not generally identically distributed is the following:  

Summing IID random vectors (example slide 3), where Sigma is the covariance matrix of each vector, we have:

Lec14.pdf Inference, estimation