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... Given a vector (c0 , c1 , · · · , cn−1 ), we can associate a polynomial naturally which is c(X) = c0 + c1 X + · · · + cn−1 X n . This is just interpretting the vector space Fnq as the additive group of the ring Fq [X]/(f (X)) where f is a polynomial of degree n, since they are both isomorphic. The r ...
... Given a vector (c0 , c1 , · · · , cn−1 ), we can associate a polynomial naturally which is c(X) = c0 + c1 X + · · · + cn−1 X n . This is just interpretting the vector space Fnq as the additive group of the ring Fq [X]/(f (X)) where f is a polynomial of degree n, since they are both isomorphic. The r ...
Chapter 1 Notes
... A matrix is said to be in reduced echelon form if all of the following properties hold true: 1. All rows consisting entirely of zeros are grouped at the bottom. 2. The leftmost nonzero number in each row is 1 (called the leading one). 3. The leading 1 of a row is to the right of the previous row's l ...
... A matrix is said to be in reduced echelon form if all of the following properties hold true: 1. All rows consisting entirely of zeros are grouped at the bottom. 2. The leftmost nonzero number in each row is 1 (called the leading one). 3. The leading 1 of a row is to the right of the previous row's l ...
Inner Product Spaces
... ****PROOF OF THIS PRODUCT BEING INNER PRODUCT GOES HERE**** ****SPECIFIC EXAMPLE GOES HERE**** 2.3. Example: Pn . Here we will describe a type of inner product on Pn which we will term a discrete inner product on Pn . Let {x1 , . . . , xn } be distinct real numbers. If p(x) is a polynomial in Pn , t ...
... ****PROOF OF THIS PRODUCT BEING INNER PRODUCT GOES HERE**** ****SPECIFIC EXAMPLE GOES HERE**** 2.3. Example: Pn . Here we will describe a type of inner product on Pn which we will term a discrete inner product on Pn . Let {x1 , . . . , xn } be distinct real numbers. If p(x) is a polynomial in Pn , t ...
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... in comparison with a straight computation of y uT. One example of a matrix with a small state space is the case where T is an upper triangular band-matrix: Ti j 0 for j − i p. In this case, the state dimension is equal to or smaller than p − 1, since only p − 1 of the previous input values need to b ...
... in comparison with a straight computation of y uT. One example of a matrix with a small state space is the case where T is an upper triangular band-matrix: Ti j 0 for j − i p. In this case, the state dimension is equal to or smaller than p − 1, since only p − 1 of the previous input values need to b ...
Higher Order GSVD for Comparison of Global mRNA Expression
... human global mRNA expression datasets are tabulated as organism-specific genes|17-arrays matrices D1 , D2 and D3 . The underlying assumption is that there exists a one-to-one mapping among the 17 columns of the three matrices but not necessarily among their rows. These matrices are transformed to th ...
... human global mRNA expression datasets are tabulated as organism-specific genes|17-arrays matrices D1 , D2 and D3 . The underlying assumption is that there exists a one-to-one mapping among the 17 columns of the three matrices but not necessarily among their rows. These matrices are transformed to th ...
