21. A nonzero scalar multiple of an identity matrix is called a " scalar " matrix. 22. The formula defines a translation if and only if " A " is the identity matrix . 23. The identity matrix of a given size is the only idempotent matrix of that size having full rank. 24. Where p and q were matrices for location and momentum p, and I is the identity matrix . 25. Where X ^ 0 is defined to be the identity matrix I with the same dimensions as X. 26. This is equivalent to saying that " A " times its transpose must be the identity matrix . 27. An alternative decomposition is into completely polarized ( zero determinant ) and unpolarized ( scaled identity matrix ) components. 28. However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots. 29. In the case of an orthonormalised basis set the overlap matrix, S, reduces to the identity matrix . 30. The matrix corresponding to this bilinear form ( see below ) on a standard basis is the identity matrix .
