Linear Algebra - Column Vector (One-column matrix)

Card Puncher Data Processing

Linear Algebra - Column Vector (One-column matrix)

About

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

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”)

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





Discover More
Card Puncher Data Processing
Linear Algebra - Matrix

The Traditional notion of a matrix is: a two-dimensional array a rectangular table of known or unknown numbers One simple role for a matrix: packing together a bunch of columns or rows Matrix...
Card Puncher Data Processing
Linear Algebra - Matrix Equation

A linear vector equation is equivalent to a matrix equation of the form : where: A is an m×n matrix, x is a column vector with n entries, and b is a column vector with m entries. A matrix...
Matrix Matrix Multplication
Linear Algebra - Matrix Matrix (Multiplication)

Matrix Matrix (Multiplication) definition . Two matrices may be multiplied when they are conformable: ie the number of columns in the first matrix is equal to the number of rows in the second matritransposevector-matrix...
Card Puncher Data Processing
Linear Algebra - Row vector (One-row matrix)

A vector is interpreted as a one-column matrix (a column vector) To become aone-row matrices, use transpose to turn a column vector into a row vector.



Share this page:
Follow us:
Task Runner