Leading diagonal

The peaks along the leading diagonal 01 =102 eorrespond to the usual absorption speetnim, whereas the eross-peaks (peaks removed from the diagonal) provide evidenee for eross-eorrelations. 

Step 2 Set up an identity matrix of the dimensions needed, n x n a matrix with l s on the leading diagonal and 0 s elsewhere. For this problem there are 5 unis so a 5 x 5 matrix is needed, Figure 4.16. 

With all the zeros along the leading diagonal, we can find relatively easily that the characteristic equation of A, sl - A = 0, is... 

Main sequence star The majority of stars, 92 per cent, that fall on the leading diagonal of the Herzprung-Russell diagram. 

Continued multiplication in pairs leads to a table of direct products (Table 2) which is symmetrical about its leading diagonal so that only... 

IN CORE AN IDENTITY MATRIX (ONES ON THE LEADING DIAGONAL) WITH DIMENSIONS EQUAL TO THE NUMBER OF UNITS "... 

IF ANY UNIT HAS A SELF-RECYCLE STREAM, THE VALUE ON THE " LEADING DIAGONAL WILL NOT BE ONE AND MUST BE TYPED IN "... 

If in a determinant the elements a and a, are equal ars=Osr) it is called symmetric, whilst if ars=—asr it is skew-symmetric. In the second case the elements of the leading diagonal are all zero (since the element =—a , which can be true only if aa=0) ... 

Use the properties of determinants to introduce as many zeros as possible to the right (or left) of the leading diagonal... 

The unit matrix is a square matrix of order n, denoted here by E , whose leading diagonal elements are all unity i.e. have value 1) and whose off-diagonal elements are zero. Thus, for example ... 

A set of first-order differential equations can be obtained by rearranging the leading diagonal terms in the square matrix on the right-hand side of (20.5). Hence -... 

Fig. 8.1. Form of the matrices % or c j for materials of different symmetries (a) hexagonal, (b) cubic, (c) isotropic. All matrices are symmetric about the leading diagonal and the following symbols are used , zero component , non-zero component — , equal components x, z(sn —Sia) for Sf/ or Cia) for...

Let us consider once more the set of constitutive equations (4.11), (4.12), and (4.13). It was mentioned in this context that partial derivatives of dependent variables with respect to independent variables define the material coefficients involved. The terms appearing in the leading diagonal of the array on the right hand side of this system of equations represent the so called principal effects. Writing... 

Matrix notation allows to represent them in the form of 6 by 6 matrices which, in general, are not symmetric abont the leading diagonal. In the triclinic crystal no coefficients vanish for symmetiy reasons and all 36 of them are independent. 

First we note that the matrices T and X in (8.2.14) are rectangular, their columns referring only to the n occupied orbitals. With the notation of (8.3.1) the n X n matrix becomes TlXi, Xi being the first block of an extended X matrix in which Xj is identically zero. In terms of the full matrices, the quantity of interest is thus simply the leading diagonal block of... 

This determinant is widely used in molecular orbital theory and should be memorized. Notice that the terms on the leading diagonal are of the form Hii — 5 n, 22 — iS 22 etc-, and that the determinant is symmetrical about the leading diagonal (since = H21 etc., and iS 12 = [Pg.19]

The line which may be drawn from top left to bottom right (and in this case containing 1, I and 9) is referred to as the leading diagonal,... 

Note that each term on the leading diagonal is jf and all the other terms are unity (for adjacent atoms) and zero (for non-adjacent atoms). 

The only nonzero terms remaining in all of the submatrices having either rs or mn = 01 are the leading diagonal terms in The equations with both... 

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