Write the standard basis for the vector space.R6
Question
Write the standard basis for the vector space.R6
Solution
The standard basis for the vector space R^6 is a set of 6 vectors, each having 6 components. These vectors are:
e1 = (1, 0, 0, 0, 0, 0) e2 = (0, 1, 0, 0, 0, 0) e3 = (0, 0, 1, 0, 0, 0) e4 = (0, 0, 0, 1, 0, 0) e5 = (0, 0, 0, 0, 1, 0) e6 = (0, 0, 0, 0, 0, 1)
Each vector has a '1' in one position and '0' in all other positions. The position of the '1' corresponds to the index of the vector in the basis. This set of vectors forms a basis because they are linearly independent and span the vector space R^6.
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