Linear Algebra and the C Language/a0ow

__NOTOC__ Dot Product In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number.... Wikipedia: Dot product Compute orthogonal vectors You want to compute the orthogonal vectors to the vectors V. To calculate these vectors, I chose the algorithm that calculates free vectors. I create a system Ab with at least two rows and I solve this system using the free variables algorithm. /* The algorithm of free variables (The free vectors: b_free) */ gj_PP_mR(Ab,NO); put_zeroR_mR(Ab,Ab_free); put_freeV_mR(Ab_free); gj_PP_mR(Ab_free,YES); c_Ab_b_mR(Ab_free,b_free); I check if the dot product of two vectors is zero; this means that they are orthogonal to each other. for(c=C0; c<VARRAY; c++) for(r=C0; r<UARRAY; r++) printf(" v^t[%d] u[%d] = %+.4f\n",c,r, dot_R(vt[c],u[r])); If you want normalize the vectors, you can find an example Here Application Compute an orthogonal vector: In ℝ2 In ℝ3 In ℝ4 Compute two orthogonal vectors: In ℝ3 In ℝ4 Compute three orthogonal vectors: In ℝ4 Compute four orthogonal vectors: In ℝ6 Compute five orthogonal vector: In ℝ6