Left division

As stated earlier, Matlab s philosophy is to read everything as a matrix. Consequently, the basic operators for multiplication, right division, left division, power (, /,, A) automatically perform corresponding matrix operations (A will be introduced shortly in the context of square matrices, / and will be discussed later, in the context of linear regression and the calculation of a pseudo inverse, see The Pseudo-Inverse, p.117). 

X=A. B Y1=A./B Y2=A. B Z=A.AB % % % 0. 0 element-wise element-wise element-wise element-wise multiplication right division left division raising to the power... 

Element-wise right division (./) leads to the inverse result of element-wise left division (. ) and the operator. A raises all elements to the corresponding power. 

The left division corresponds to a simple [4 + 2] cycloaddition, whereas the right division corresponds to a complex reaction involving formation of three ring bonds at once. Actual Diels-Alder reactions require diene and dienophile starting materials, and two possibilities, using 1,3-cyclopentadiene as the diene and ethene or ethyne as dienophile, follow ... 

Addition Subtraction Multiplication Transpose Inverse Determinant Eigenvalues Matrix left division (uses Gauss elimination to solve a set of linear equations)... 

We will first use the MATLAB matrk left division operator to solve this problem. The operator solves the problem usii the Gauss elimination. We then solve the problem using the inv command. 

Fig. 9.4a,b. A 31-year-old woman with PPH (a). Selective angiogram of the inferior mesenteric artery (IMA) showed the left colic artery supplying the uterus (arrows), b Early phase of selective angiogram of the IMA shows that the second left division feeds exclusively the uterus (arrow). (Courtesy of Patrick Garance)... 

The operation is the left division and / is right division. In this case, left division is used since the matrix A is to the left of vector b. You can learn about these operations in MATLAB by entering help slash. The right division B/A computes (A /B ) again using LU factorization and Guassian eliminination. 

Left Division of the furnace into Hottel zones for the furnace calculation. Right Two-dimensional cross section of the non-structured furnace and reactor tube integration grids. 

Table 10.1 enumerates the MATLAB operators. Most of these are the same as for Excel and VBA. A notable difference is the backslash operator (called left division), which is used primarily when solving sets of linear algebraic equations. Examples using this operator appear in the sequel. 

The main stem of the nitrometer widens into a bulb and then narrows to form a graduated tube. The usual graduation is of 8 ml. in o o2 ml. divisions. The graduations continue to the tap Tj at the top of the stem. Above Tj there is a small reservoir H to prevent splashing of the concentrated alkali when gas is expelled from the nitrometer and also to ensure that a small excess of potash is left as a liquid seal above the tap T ,. 

Division of matrices is not defined, but the equivalent operation of multiplieation by an inverse matrix (if it exists) is defined. If a matr ix A is multiplied by its own inverse matrix, A , the unit matrix I is obtained. The unit matrix has Is on its prineipal diagonal (the longest diagonal from upper left to lower right) and Os elsewhere for example, a 3 x 3 unit matrix is... 

Figure 14-33. Gas engine driven parallel compression cylinders in process gas plant service. Note that the front side of gas engines are on the right with high-pressure compressor cylinders extending horizontally left. Also note the suction side pulsation drums on top of compressor cylinders, mid-way. (Used by permission Cooper-Cameron Corporation, Reciprocating Products Division.)...

Thus, the inverse matrix plays the role of division in matrix algebra. Multiplication of equation (1.33) from the left by B and from the right by C yields... 

If the order of q(s) is higher, we need first carry out "long division" until we are left with a partial fraction "residue." Thus the coefficients ai are also called residues. We then expand this... 

Figure 16-2 A cloth filter. The dirty air enters in the side near the bottom as shown in the figure on the left. The large particles drop to the bottom. The small particles are carried upward and deposited on the exterior surface of bag (shown in black).The air passesthrough the bag and exits through the exhaust plenum. The bags are cleaned periodically, but only a few at a time. When this occurs the exhaust plenum is closed as shown in the figure on the right. A burst of air is admitted to the inside of the bags this knocks the small particles off the sides and they settle to the bottom where they are discharged through a rotary valve. Courtesy of the Dustex Division of American Precision Industries, Inc.

Schmidt What happens to the six cortical divisions in the p27 deficient mice Likewise, has anyone ever done the heroic thing of taking the basal layer that gives rise to the six cortical divisions and transplanting it down one day to see whether it still has five divisions left ... 

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