Some linear algebra
ثبت نشده
چکیده
defined for all complex numbers λ, where I denotes the � × � identity matrix. It is not hard to see that a complex number λ is an eigenvalue of A if and only if χA(λ) = 0. We see by direct computation that χA is an �th-order polynomial. Therefore, A has precisely � eigenvalues, thanks to the fundamental theorem of algebra. We can write them as λ1� � � � � λ�, or sometimes more precisely as λ1(A)� � � � � λ�(A).
منابع مشابه
Some results on Haar wavelets matrix through linear algebra
Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.
متن کاملLinear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras
Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.
متن کاملWeak amenability of (2N)-th dual of a Banach algebra
In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.
متن کاملSome notes on L-projections on Fourier-Stieltjes algebras
In this paper, we investigate the relation between L-projections and conditional expectations on subalgebras of the Fourier Stieltjes algebra B(G), and we will show that compactness of G plays an important role in this relation.
متن کاملLinear combinations of wave packet frames for L^2(R^d)
In this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for L2(Rd). Further, we illustrate our results with some examples and applications.
متن کاملA note on the new basis in the mod 2 Steenrod algebra
The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations, denoted by $Sq^n$, between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space. Regarding to its vector space structure over $mathbb{Z}_2$, it has many base systems and some of the base systems can also be restricted to its sub algebras. On the contrary, in ...
متن کامل