Linear Algebra - Column Vector (One-column matrix)

> Linear Algebra

1 - About

A vector can be (seen|interpreted) as a one-column matrix. To get a one-row matrix, use transpose.

Advertising

3 - Multiplication with a matrix

Multiplying a matrix A by a one-column matrix B:

<MATH>A * b = \begin{bmatrix}\begin{array}{rrr} & & \\ & \large{A} & \\ & & & \end{array}\end{bmatrix} * \begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}</MATH>

By matrix-vector definition of matrix-matrix multiplication, result is:

  • a matrix with one column: A * b
  • that you can interpret as a vector (a “column vector”)

4 - Convention

  • Write vector <math>[1, 2, 3]</math> as <math>\begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}</math>
  • Write <math>A * [1, 2, 3]</math> as <math>\begin{bmatrix}\begin{array}{ccc} & & \\ & \large{A} & \\ & & & \end{array}\end{bmatrix} * \begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}</math> or A*b
linear_algebra/column_vector.txt · Last modified: 2013/08/21 17:05 by gerardnico