Index notation greatly simplifies the manipulation of [[tensor]]s. A commonly used convention when dealing with tensors is the so called "Einstein summation convention." Any index that is repeated exactly twice is assumed to be summed over and the sum symbols are not written.<ref>[http://mathworld.wolfram.com/EinsteinSummation.html Einstein Summation Convention at mathworld.wolfram.com]</ref> In the example above, the sum:
+
Index notation greatly simplifies the manipulation of [[tensor]]s. A commonly used convention when dealing with tensors is the so-called "Einstein summation convention." Any index that is repeated exactly twice is assumed to be summed over and the sum symbols are not written.<ref>[http://mathworld.wolfram.com/EinsteinSummation.html Einstein Summation Convention at mathworld.wolfram.com]</ref> In the example above, the sum: