| 21. | Alternatively, a near-field is a near-ring in which there is a multiplicative identity, and every non-zero element has a multiplicative inverse.
|
| 22. | Instead, the mapping is from the space to the zero element in ! ( just the ordinary zero 0 ):
|
| 23. | They form a ring, that is, one can multiply, add and subtract them, but not always divide by a non-zero element.
|
| 24. | Its standard basis, consisting of the sequences having only one non-zero element, which is equal to 1, is a countable Hamel basis.
|
| 25. | In general the zero element of a ring is unique and typically denoted as 0 without any subscript indicating the parent ring.
|
| 26. | To define them he uses diagonal matrices " A ij " having only + 1 or " 1 for non-zero elements.
|
| 27. | Bulu?" et al . " present a sparse matrix data structure that Z-orders its non-zero elements to enable parallel matrix-vector multiplication.
|
| 28. | One can always divide any non-zero element of a Hilbert space by its norm and obtain a " normalized " state vector.
|
| 29. | In general the zero element of a ring is unique and typically denoted as 0 without any subscript to indicate the parent ring.
|
| 30. | In a null set is the set with zero elements; and in measure theory, a null set is a set with zero measure.
|
