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}.

Read more about this topic:  Column Vector

Famous quotes containing the word operations:

    “Plot, rules, nor even poetry, are not half so great beauties in tragedy or comedy as a just imitation of nature, of character, of the passions and their operations in diversified situations.”
    —Horace Walpole (1717–1797)

    “It may seem strange that any road through such a wilderness should be passable, even in winter, when the snow is three or four feet deep, but at that season, wherever lumbering operations are actively carried on, teams are continually passing on the single track, and it becomes as smooth almost as a railway.”
    —Henry David Thoreau (1817–1862)

    “You can’t have operations without screams. Pain and the knife—they’re inseparable.”
    —Jean Scott Rogers. Robert Day. Mr. Blount (Frank Pettingell)