Null matrix

Living calculated the integrals, we are now ready to start the SCF calculation. To formulate the Fock mahix it is necessary to have an initial guess of the density matrix, P. The simplest approach is to use the null matrix in which all elements are zero. In this initial step the Fock nulrix F is therefore equal to... 

We shall denote the zero matrix as 0, not 0 or O. The zero matrix is sometimes called the null matrix. 

Perform the subtraction and addition above and multiply the resultant matrices to show that the null matrix is obtained. 

Null matrix This has all elements equal to zero. 

Special matrices are the null matrix 0 in which all elements are zero, and the sum matrix 1 in which all elements are unity. In the case of 3x3 matrices we obtain ... 

The product of an arbitrary m X n matrix A with a conformable n X p null matrix is the mX p null matrix... 

The unit matrix (German Einheit) is one which is diagonal with all of the diagonal elements equal to one. It plays the role of unity in matrix algebra. Clearly, the unit matrix multiplied by a constant yields a diagonal matrix with all of die diagonal elements equal to the value of the constant. If the constant is equal to zero, the matrix is the null matrix 0, with all elements equal to zero. 

Note that the right-hand side of this expression is an E x I null matrix, and thus element conservation must hold for any choice of e e l,E and i e 1Moreover, since the element matrix is constant, (5.10) can be applied to the scalar transport equation ((1.28), p. 16) in order to eliminate the chemical source term in at least E of the K equations.9 The chemically reacting flow problem can thus be described by only K - E transport equations for the chemically reacting scalars, and E transport equations for non-reacting (conserved) scalars.10... 

Both S, by definition, and F through equation (4.4.12), are centered, i.e., their expectation is a null matrix. Therefore the sample covariance matrix between the reduced data and the components is... 

We may now combine these matrices to obtain the null matrix... 

State whether each of the following concepts is applicable to all matrices or to only square matrices (a) real matrix (b) symmetric matrix (c) diagonal matrix (d) null matrix (e) unit matrix (f) Hermitian matrix (g) orthogonal matrix (h) transpose (i) inverse (j) Hermitian conjugate (k) eigenvalues. 

A matrix with every element equal to zero is called a null matrix and is symbolized by 0. 

Since Fz, F7 are inequivalent representations (Tz not I1), Lemma 3 requires that M is the null matrix. Therefore,... 

The zero matrix or null matrix, 0, is any matrix with all its elements zero. Examples ... 

In matrix algebra it is possible for the product of two conformable matrices, neither of which is a null matrix, to be a null matrix. For example, if A and B are... 

A systematic diffraction study was made with both neutrons and x-rays of metal- hydride systems in the composition range of 2 to 66.5 atomic % hydrogen of hafnium, titanium, and zirconium, and a nuclear null-matrix consisting of 62 atomic % titanium and 38 atomic % zirconium, with emphasis on the metal-rich regions. A nuclear null-matrix as defined here consists of two or more types of nuclei in which some of the nuclei scatter thermal neutrons 180° out of phase with others, such that the resultant structure factor is zero. 

Since the hypotheses allow for A to be a null matrix, the theorem is of limited value. If irreducibility is added, a stronger theorem applies. 

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