Definitions

Definitions

Matrix:

A 2-dimensional array of real numbers
An m by n matrix has m rows and n columns
$\begin{eqnarraystar} A_{m \times n} & = & \left[ \begin{array} {cccc} a_{11} &... ... \ a_{m1} & a_{m2} & \cdots & a_{mn} \end{array} \right] \end{eqnarraystar}$
A[i,j] = a_ij, element at ith row and jth column.

Vector:

A 1-dimensional array of real numbers
A row vector (of size n) -- a matrix with 1 row $\begin{eqnarraystar} u^T & = & \left[ u_1 \; u_2 \; \cdots \; u_n \right] \end{eqnarraystar}$
A column vector (of size m) -- a matrix with 1 column $\begin{eqnarraystar} v & = & \left[ \begin{array} {c} v_1 \ v_2 \ \vdots \ v_m \end{array} \right] \end{eqnarraystar}$
By default, a vector is a column vector

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