| 11. | Let both of and be 3-dimensional column vectors, represented as follows,
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| 12. | Where the vector \ mathbf { 1 } is a column vector of ones.
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| 13. | Here is thought of as a column vector containing components with the allowed values of.
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| 14. | In components, such operator is expressed with orthogonal matrix that is multiplied to column vectors.
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| 15. | Again, is thought of as a column vector containing components with the allowed values of.
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| 16. | This matrix must be the product of a single column vector with a single row vector.
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| 17. | This produces a basis for the column space that is a subset of the original column vectors.
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| 18. | Another important example is the transpose operation in linear algebra which takes row vectors to column vectors.
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| 19. | In this case, our data vector, d is a column vector of dimension ( 5x1 ).
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| 20. | Here, \ mathbf { 1 } is a column vector of 1's of dimension M.
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