let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

Let ‎X be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎Cartesian decomposition ‎‎X = A + i ‎B‎‎‎‎‎, ‎where ‎‎A ‎and ‎‎B ‎are ‎‎‎n ‎‎times n‎ ‎Hermitian ‎matrices. ‎It ‎is ‎known ‎that ‎‎$Vert X Vert_p^2 ‎leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎Vert . Vert_p$ ‎is ‎the ‎Schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎In this paper‎, this inequality and some of its improvements ...

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

Here, we will provide a spectral norm bound for the error of the approximation constructed by the BasicMatrixMultiplication algorithm. Recall that, given as input a m × n matrix A and an n× p matrix B, this algorithm randomly samples c columns of A and the corresponding rows of B to construct a m× c matrix C and a c× p matrix R such that CR ≈ AB, in the sense that some matrix norm ||AB −CR|| is...

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

Let A be a complex m × n matrix. We find simple and good lower bounds for its spectral norm ‖A‖ = max{ ‖Ax‖ | x ∈ C, ‖x‖ = 1 } by choosing x smartly. Here ‖ · ‖ applied to a vector denotes the Euclidean norm.

where B ∈ C, C ∈ C are fixed matrices and ∆ is an element of a subset ∆ of C. It is assumed that ∆ is closed, connected and contains the zero matrix. The size of a perturbation ∆ ∈ ∆ is measured by a norm ‖ · ‖ on C. (a) The structued pseudospectrum (also called spectral value set) of the triple (A,B,C) with respect to the perturbation class ∆, the underlying norm ‖ · ‖ and the perturbation lev...

The spectral radius of every d× d matrix A is bounded from below by c ‖A‖ ‖A‖, where c = c(d) > 0 is a constant and ‖·‖ is any operator norm. We prove an inequality that generalizes this elementary fact and involves an arbitrary number of matrices. In the proof we use geometric invariant theory. The generalized spectral radius theorem of Berger and Wang is an immediate consequence of our inequa...

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...