Category: Matrix and Signal Processing

If you can, answer the question below: Write your answer in the comment box. Show linear vector space using matrix-vector multiplication. y = AC = [a1 a2 a3…an] * [c1 c2 c3 …. cn]. [c1 c2 c3 …. cn] is in column form

If you can, answer the question below: Write your answer in the comment box. Vector Space S = { y varepsilon R^m | y = Ac, c varepsilon R^n }

If you can, answer the question below: Write your answer in the comment box. What is the dimension of S?

If you can, answer the question below: Write your answer in the comment box. Can we say that the number of independent directions that the space S spans to be the dimension of S?

If you can, answer the question below: Write your answer in the comment box. What is the dimension of the universe that we live in?

If you can, answer the question below: Write your answer in the comment box. is dim(S) = n?

If you can, answer the question below: Write your answer in the comment box. What is the dimension of a plane?

If you can, answer the question below: Write your answer in the comment box. If we take one more vector orthogonal to the plane, then what will be the dimension?

If you can, answer the question below: Write your answer in the comment box. Define/describe Linear vector space in terms of the vectors [a_1, a_2, …., a_n]

If you can, answer the question below: Write your answer in the comment box. In the above case, if x and y are vectors in S, Does x + y belong to S?

If you can, answer the question below: Write your answer in the comment box. In the above case, if x is a vector in S, does cx belong to S? c is in R

If you can, answer the question below: Write your answer in the comment box. Give more rigorous mathematical notation of Linear Vector Space.

If you can, answer the question below: Write your answer in the comment box. What is the notation to represent a vector of real numbers or real-complex numbers?

If you can, answer the question below: Write your answer in the comment box. Upper case bold letter — matrix or scalar or vector?

If you can, answer the question below: Write your answer in the comment box. Upper case non-bold letter — matrix or scalar or vector?

If you can, answer the question below: Write your answer in the comment box. Is a vector usually a column vector? what is the ith column in a Matrix A? $a_i$ what does it mean? $a_j^T$ what does it mean? How is the $j^th$ element represented?

If you can, answer the question below: Write your answer in the comment box. What do you mean by the concept of vector space?

If you can, answer the question below: Write your answer in the comment box. What are bases?

If you can, answer the question below: Write your answer in the comment box. What do you mean by Linear Vector Spaces?

If you can, answer the question below: Write your answer in the comment box. If S is a linear vector space, what are the properties of S?

If you can, answer the question below: Write your answer in the comment box. What do you mean by matrix dimensions?

If you can, answer the question below: Write your answer in the comment box. Can you represent a matrix of real numbers with m * n dimensions with notations?

If you can, answer the question below: Write your answer in the comment box. Can you represent a matrix of complex numbers with m * n dimensions with notations?

If you can, answer the question below: Write your answer in the comment box. What is the outcome of matrix multiplications? is the multiplication outcome a number?

If you can, answer the question below: Write your answer in the comment box. What are tall matrices? What are short matrices?

If you can, answer the question below: Write your answer in the comment box. What is a square matrix?

If you can, answer the question below: Write your answer in the comment box. What is a diagonal matrix?

If you can, answer the question below: Write your answer in the comment box. What does dimension mean for a single vector?

If you can, answer the question below: Write your answer in the comment box. What are the various interpretations of matrix multiplication operations?

If you can, answer the question below: Write your answer in the comment box. What are matrix determinants?

If you can, answer the question below: Write your answer in the comment box. What is the significance of matrix determinants?

If you can, answer the question below: Write your answer in the comment box. What is linear dependence?

If you can, answer the question below: Write your answer in the comment box. What is a subspace?

If you can, answer the question below: Write your answer in the comment box. What are the related ideas of subspace?

If you can, answer the question below: Write your answer in the comment box. What is a row space?

If you can, answer the question below: Write your answer in the comment box. What is a column space?

If you can, answer the question below: Write your answer in the comment box. What is the rank of a matrix?

If you can, answer the question below: Write your answer in the comment box. What is a vector norm?

If you can, answer the question below: Write your answer in the comment box. What are the different types of Matrix multiplication?

If you can, answer the question below: Write your answer in the comment box. What is the Big Block perspective of Matrix Multiplication?

If you can, answer the question below: Write your answer in the comment box. Do the multiplication approaches apply to the big block cases? and/or vice versa.

If you can, answer the question below: Write your answer in the comment box. What is linear independence?

If you can, answer the question below: Write your answer in the comment box. Give some examples of Auto-Regressive Processes?

If you can, answer the question below: Write your answer in the comment box. What is the relation between Auto-Regressive Process and Toeplitz systems?

If you can, answer the question below: Write your answer in the comment box. Can we say that voice and video signals, sinewaves-plus-noise, signals in control systems and signals induced by earthquakes are some examples of Auto-Regressive Processes?

If you can, answer the question below: Write your answer in the comment box. What is Levinson Durbin Recursion?

If you can, answer the question below: Write your answer in the comment box. Difference: Auto-Regressive and Auto Correlation.

If you can, answer the question below: Write your answer in the comment box. What is a lattice filter structure?

If you can, answer the question below: Write your answer in the comment box. Can you utilize the structure of a Toeplitz matrix to find solutions that have lower algorithmic (flops, operation count) complexity?

If you can, answer the question below: Write your answer in the comment box. What is adaptive filtering?

If you can, answer the question below: Write your answer in the comment box. What is an AR system?

If you can, answer the question below: Write your answer in the comment box. What do the covariance matrices of Stationary signals look?

If you can, answer the question below: Write your answer in the comment box. Can you solve Toeplitz systems using Gaussian elimination?

If you can, answer the question below: Write your answer in the comment box. How does a Toeplitz Matrix relate to Stationary or non-stationary signals?

If you can, answer the question below: Write your answer in the comment box. What is Gaussian elimination?

If you can, answer the question below: Write your answer in the comment box. Can you solve Toeplitz systems using Cholesky Methods?

If you can, answer the question below: Write your answer in the comment box. If you solve Toeplitz systems using Gaussian Eliminations, what is the algorithmic complexity (algorithm)?

If you can, answer the question below: Write your answer in the comment box. Define Cholesky Methods?

If you can, answer the question below: Write your answer in the comment box. What is a Toeplitz Matrix?

If you can, answer the question below: Write your answer in the comment box. Will in a Toeplitz Matrix, the elements parallel to the diagonal be the same? If so, how?

If you can, answer the question below: Write your answer in the comment box. What is a Toeplitz Matrix?

If you can, answer the question below: Write your answer in the comment box. Will in a Toeplitz Matrix, all elements in a diagonal be the same? If so, how i.e. give examples?

If you can, answer the question below: Write your answer in the comment box. Give examples?

If you can, answer the question below: Write your answer in the comment box. What is regularization?

If you can, answer the question below: Write your answer in the comment box. What is LMS algorithm? Linear Mean Square.

If you can, answer the question below: Write your answer in the comment box. What is the role of QR decomposition in LS analysis?

If you can, answer the question below: Write your answer in the comment box. What is QR decomposition?

If you can, answer the question below: Write your answer in the comment box. PLS and Machine Learning. How are they related?

If you can, answer the question below: Write your answer in the comment box. What is PLS? Partial Least Square?

If you can, answer the question below: Write your answer in the comment box. What is principle component analysis?

If you can, answer the question below: Write your answer in the comment box. What is Linear Least Square?

If you can, answer the question below: Write your answer in the comment box. What are Generalized Eigenvalues?

If you can, answer the question below: Write your answer in the comment box. What is an Ordinary LS?

If you can, answer the question below: Write your answer in the comment box. Give examples of Linear Least Square?

If you can, answer the question below: Write your answer in the comment box. What are pseudoinverses?

If you can, answer the question below: Write your answer in the comment box. What is whitening?

If you can, answer the question below: Write your answer in the comment box. What is a Quadratic Form?

If you can, answer the question below: Write your answer in the comment box. What is Gaussian Elimination?

If you can, answer the question below: Write your answer in the comment box. Derive the Gaussian Eliminataion?

If you can, answer the question below: Write your answer in the comment box. Give an example of Gaussian Elimination?

If you can, answer the question below: Write your answer in the comment box. Give an example of SVD.