The Inner Product and Conjugate of Matrix of Complex Numbers

نویسندگان

  • Wenpai Chang
  • Hiroshi Yamazaki
  • Yatsuka Nakamura
چکیده

Concepts of the inner product and conjugate of matrix of complex numbers are defined here. Operations such as addition, subtraction, scalar multiplication and inner product are introduced using correspondent definitions of the conjugate of a matrix of a complex field. Many equations for such operations consist like a case of the conjugate of matrix of a field and some operations on the set of sum of complex numbers are introduced.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

متن کامل

Properties of matrices with numerical ranges in a sector

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

متن کامل

Lecture 8 : Eigenvalues and Eigenvectors

Hermitian Matrices It is simpler to begin with matrices with complex numbers. Let x = a + ib, where a, b are real numbers, and i = √ −1. Then, x∗ = a− ib is the complex conjugate of x. In the discussion below, all matrices and numbers are complex-valued unless stated otherwise. Let M be an n× n square matrix with complex entries. Then, λ is an eigenvalue of M if there is a non-zero vector ~v su...

متن کامل

ON CONEIGENVALUES OF A COMPLEX SQUARE MATRIX

In this paper, we show that a matrix A in Mn(C) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. And also show that if allconeigenvalues of conjugate-normal matrix A be real, then it is symmetric.  

متن کامل

Evaluation of wall thickness and porosity effects on the conjugate free convection heat transfer rate of hybrid nanofluid inside a square cavity

At present study, effects of wall thickness and porosity on the conjugate free convection heat transfer inside a square cavity have been examined. Continuity, momentum and energy equations for fluid and solid matrix phases are governing equations in present work. Mentioned equations and related boundary conditions have been transformed into their non-dimensional forms. They are solved using fin...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007