The Multivariate Gaussian Distribution
... − 21 (x − µ)T Σ−1 (x − µ), is a quadratic form in the vector variable x. Since Σ is positive definite, and since the inverse of any positive definite matrix is also positive definite, then for any non-zero vector z, z T Σ−1 z > 0. This implies that for any vector x 6= µ, (x − µ)T Σ−1 (x − µ) > 0 ...
... − 21 (x − µ)T Σ−1 (x − µ), is a quadratic form in the vector variable x. Since Σ is positive definite, and since the inverse of any positive definite matrix is also positive definite, then for any non-zero vector z, z T Σ−1 z > 0. This implies that for any vector x 6= µ, (x − µ)T Σ−1 (x − µ) > 0 ...
1 Notes on directed graph analysis of accounting Directed graphs
... Ay = x A is an incidence matrix which has a row for every account and a column for every journal entry. An incidence matrix, a matrix in which every column consists of zeros, a positive one, and a negative one, is well-suited to capture the mechanics of the double entry system; the one in the column ...
... Ay = x A is an incidence matrix which has a row for every account and a column for every journal entry. An incidence matrix, a matrix in which every column consists of zeros, a positive one, and a negative one, is well-suited to capture the mechanics of the double entry system; the one in the column ...
Reduced Row Echelon Form
... For some reason our text fails to define rref (Reduced Row Echelon Form) and so we define it here. Most graphing calculators (TI-83 for example) have a rref function which will transform any matrix into reduced row echelon form using the so called elementary row operations. We will use Scilab notati ...
... For some reason our text fails to define rref (Reduced Row Echelon Form) and so we define it here. Most graphing calculators (TI-83 for example) have a rref function which will transform any matrix into reduced row echelon form using the so called elementary row operations. We will use Scilab notati ...
ECO4112F Section 5 Eigenvalues and eigenvectors
... with two different eigenvalues; by Proposition 3 A is a d-matrix. Now let x and y be eigenvectors of A corresponding to the eigenvalues 2 and −1 respectively. By Proposition 2, x and y are linearly independent. Hence, by the proof of Proposition 1 we may write S−1 AS = D where D =diag(2, −1) and S ...
... with two different eigenvalues; by Proposition 3 A is a d-matrix. Now let x and y be eigenvectors of A corresponding to the eigenvalues 2 and −1 respectively. By Proposition 2, x and y are linearly independent. Hence, by the proof of Proposition 1 we may write S−1 AS = D where D =diag(2, −1) and S ...
MATH1022 ANSWERS TO TUTORIAL EXERCISES III 1. G is closed
... 2. From Exercises II Qus 4, 5 we know that T ET and HEX are groups of order 12. They are non-abelian since in T ET , for example, the products of the rotation through 2π/3 fixing A, and which takes B to C to D and back to B, and that through 2π/3 fixing B, and which takes A to C to D and back to A, ...
... 2. From Exercises II Qus 4, 5 we know that T ET and HEX are groups of order 12. They are non-abelian since in T ET , for example, the products of the rotation through 2π/3 fixing A, and which takes B to C to D and back to B, and that through 2π/3 fixing B, and which takes A to C to D and back to A, ...