Numerical Range of Moore–Penrose Inverse Matrices

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Numerical Range for Random Matrices

We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. In particular, numerical range of complex Ginibre matrix almost surely converges to the disk of radius √ 2. Since the spectrum of non-hermitian random...

A Symmetric Numerical Range for Matrices

For each norm v on <en, we define a numerical range Z., which is symmetric in the sense that Z. =Z"D, where vD is the dual norm. We prove that, for aE <enn, Z.(a) contains the classical field of values V(a). In the special case that v is the lcnorm, Z.(a) is contained in a set G(a) of Gershgorin type defined by C. R. Johnson. When a is in the complex linear span of both the Hennitians and the v...

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

Positive definiteness of tridiagonal matrices via the numerical range