mathematics 217 notes
... The characteristic polynomial of an n×n matrix A is the polynomial χA (λ) = det(λI −A), a monic polynomial of degree n; a monic polynomial in the variable λ is just a polynomial with leading term λn . Note that similar matrices have the same characteristic polynomial, since det(λI − C −1 AC) = det C ...
... The characteristic polynomial of an n×n matrix A is the polynomial χA (λ) = det(λI −A), a monic polynomial of degree n; a monic polynomial in the variable λ is just a polynomial with leading term λn . Note that similar matrices have the same characteristic polynomial, since det(λI − C −1 AC) = det C ...
Eigenvalue equalities for ordinary and Hadamard products of
... When A and B are real, the two sets of inequalities coniside. However, for complex A and B, as mentioned in [5, p.315], the eigenvalues of AB and AB T may not be the same and they provide different lower bounds in (5) and (6). In Section 5, using a result in Section 4, we determine their equality fo ...
... When A and B are real, the two sets of inequalities coniside. However, for complex A and B, as mentioned in [5, p.315], the eigenvalues of AB and AB T may not be the same and they provide different lower bounds in (5) and (6). In Section 5, using a result in Section 4, we determine their equality fo ...
Matrix Groups - Bard Math Site
... The general linear group GL(n, F ) is the most general matrix group, in the same way that Sn is the most general permutation group. In particular, every matrix group is just a subgroup of some GL(n, F ). The most important subgroup of GL(n, F ) is the special linear group. Definition: The Special Li ...
... The general linear group GL(n, F ) is the most general matrix group, in the same way that Sn is the most general permutation group. In particular, every matrix group is just a subgroup of some GL(n, F ). The most important subgroup of GL(n, F ) is the special linear group. Definition: The Special Li ...
