+ This Gram-Schmidt routine can be used on matrices as well, so long
+ as an appropriate inner-product is provided::
+
+ sage: E11 = matrix(QQ, [ [1,0],
+ ....: [0,0] ])
+ sage: E12 = matrix(QQ, [ [0,1],
+ ....: [1,0] ])
+ sage: E22 = matrix(QQ, [ [0,0],
+ ....: [0,1] ])
+ sage: I = matrix.identity(QQ,2)
+ sage: trace_ip = lambda X,Y: (X*Y).trace()
+ sage: gram_schmidt([E11,E12,I,E22], inner_product=trace_ip)
+ [
+ [1 0] [ 0 1/2*sqrt(2)] [0 0]
+ [0 0], [1/2*sqrt(2) 0], [0 1]
+ ]
+