Commutative property

The commutation properties of the components of L allow us to conclude that... 

These operators have the following commutation properties... 

Here we have used the symmetry and commuting properties of the matrices to obtain the final line. This shows that the correlation matrix goes like... 

COMMUTATIVE PROPERTY states that when performing a string of addition operations, or a string of multiplication operations, the order does not matter. In other words, a + b = b + a. 

Recall that the order of operations directs you to add or multiply working from left to right. When you balance your checkbook, and have to add up a string of outstanding checks, list them all and use the commutative property to arrive at the total. Then, change the order of addends to add pairs whose unit (ones) digit adds to ten. 

In the same way, the commutative property is helpful when multiplying several numbers or terms. Change the order to find pairs of numbers whose product would be 10, 100, or 1,000. 

The commutative property deals with the ORDER of the terms. 

Which choice below shows an example of the commutative property ... 

This general non-commutative property of matrix multiplications is in contrast with ordinary algebra. 

Using only the above commutation properties, it is possible to prove important... 

This property follows from the associative and commutative properties if we allow the concept of a differentiation operator <5 that performs its function by convolution. We see that... 

In this equation, the image value im is the mth sample of the smeared version of ok. We transform the subscripts in an obvious way that recognizes the commutative property of convolution and considers only spread functions that are nonvanishing over some finite domain having an odd number of points. We may then write... 

The property of proportions that allows you to cross-multiply and have a true statement is the same property that allows for reducing across the proportion horizontally. Both of these clever tools are due to the commutative property of multiplication — the fact that reversing the order of the numbers in a multiplication property doesn t change the answer. It s just neat that this property comes in so handy when working with proportions. In the following proportion, the two numerators are each divisible by 11. Then you see that the two numbers in the right fraction are divisible by 7. Reduce that fraction so that, when you cross-multiply, you don t have to multiply by 63. 

Because of this commutative property, we can use Theorem I (Appendix A.7.1(l)) and write ... 

Whereas matrix addition (9.8) and scalar multiplication (9.9) have the usual associative and commutative properties of their scalar analogs, matrix multiplication (9.11), although associative [i.e., A(BC) = (AB)C], is inherently ncommutative [i.e., AB BAJ. This noncommutativity leads to some of the most characteristic and surprising features of matrix algebra, and underlies the still more surprising matrix-algebraic features of quantum theory. 

Using the commutation properties of the Pauli spin matrices, eqs. (22), determine U as sy, apart from a phase factor exp(iy) which has no effect on eq. (22). 

Commutative Property of Addition. When using addition, the order of the addends does not affect the sum ... 

Commutative Property of Multiplication. When using multiplication, the order of the factors does not affect the product ... 

Which equation illustrates the commutative property of multiplication ... 

The partial recovery of the quantum phase coherence of nuclear dipoles originates from the non-commutative property of the Zeeman energy with the quantum operator which represents the residual interaction after rotating the spins. This rotation has no effect on the magnetisation dynamics when the residual interaction, hHR, is equal to zero. No... 

Obviously the zero values of the angular variables define the unity matrix of the 50(4) group ea is the complete antisymmetric - Levi-Civita - tensor. The commutation properties of the infinitesimal operators defined in this manner are... 

This shows that the spinors defined in Eq. (P. 16) are eigenvectors of matrix (P.9). As a consequence, and in view of the commutation property (P.12), these spinors, which are eigenvectors of matrix (P.9) also must be eigenvectors of matrix (P.8). 

The commutation properties of [Pg.78]

The nine terms arising from (8.110), are reduced by commutation properties to six, given below each contains the product of matrix elements of L which we denote by the symbol A ... 

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