We do not expect to be able to find a solution if the predicted codimension, i . e . the number of " independent " constraints, exceeds " N " ( in the linear algebra case, there is always a " trivial ", null vector solution, which is therefore discounted ).
32.
The set of real scalar multiples of this null vector, called a " null line " through the origin, represents a " line of sight " from an observer at a particular place and time ( an arbitrary event we can identify with the origin of Minkowski spacetime ) to various distant objects, such as stars.
33.
More precisely, we consider expressions that's built of ( integer constants ) rational constants, the null vector constant, scalar variables, vector variables, addition and multiplication of scalar expressions, addition of vector expressions, multiplication of a scalar expression with a vector expression, inner product of two vector expressions, and cross product of two vector expressions.
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