21. Here is the composite Lorentz factor, and and are 3? column vectors proportional to the composite velocities. 22. For more on the treatment of row vectors and column vectors of multivariable functions, see matrix calculus. 23. So what precisely constitutes a " column vector " ( or spinor ) also depends on such arbitrary choices. 24. The dimensions of the row and column spaces equals the number of entries in the row or column vector . 25. The column vector gives the Fourier co-efficients for all points on the grid at a given frequency. 26. The matrix transformations mount up to the left in this use of a column vector for input to matrix transformation. 27. Point coordinates may be written as column vectors , T, with colons,, or with a subscript,. 28. Using column vector representation of ( reciprocal ) primitive vectors, the formulae above can be rewritten using matrix inversion: 29. To solve for the transformation parameters the equation above can be rewritten to gather the unknowns into a column vector . 30. The application of the Gram Schmidt process to the column vectors of a full column orthogonal and a triangular matrix ).
