It is common to superimpose the coordinate systems for the undeformed and deformed configurations, which results in 0 } }, and the direction cosines become Kronecker deltas:
32.
The second version has nonzero components that are } }, which results in the explicit scaling factors in " ?Properties of generalized Kronecker delta " below disappearing.
33.
Where is the Kronecker delta, is the Liouville function, is the number of distinct prime divisors of, and is the number of prime factors of, counted with multiplicity.
34.
The Kronecker delta in the expression ensures that ? 1 = ?'1, so by ordering the configurations appropriately we may cast " A " as a block diagonal matrix:
35.
This can be useful when manipulating indices, such as using index notation to verify vector calculus identities or identities of the Kronecker delta and Levi-Civita symbol ( see also below ).
36.
It is common to superimpose the coordinate systems for the undeformed and deformed configurations, which results in \ \ mathbf b = 0, and the direction cosines become Kronecker deltas, i . e.
37.
If the Kronecker delta were a tensor then the metric tensor would be equal to the Kronecker delta in all co-ordinate systems . talk ) 11 : 50, 8 March 2012 ( UTC)
38.
If the Kronecker delta were a tensor then the metric tensor would be equal to the Kronecker delta in all co-ordinate systems . talk ) 11 : 50, 8 March 2012 ( UTC)
39.
The matrices satisfying the above commutation relations are the same as for spins " a " and " b " have components given by multiplying Kronecker delta values with angular momentum matrix elements:
40.
It is common to superimpose the coordinate systems for the deformed and undeformed configurations, which results in \ mathbf b = 0 \, \ !, and the direction cosines become Kronecker deltas, i . e.
