Column Vector - Operations

Operations

  • Matrix multiplication involves the action of multiplying each row vector of one matrix by each column vector of another matrix.
  • The dot product of two vectors a and b is equivalent to multiplying the row vector representation of a by the column vector representation of b:
\mathbf{a} \cdot \mathbf{b} = \mathbf{a}^\mathrm{T} \mathbf{b} = \begin{bmatrix} a_1 & a_2 & a_3 \end{bmatrix}\begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}.

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