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rank

LinearAlgebra shark 1 min read

Definition: the number of linear independent columns of matrix M \in \mathbb{R}^{m \times n}, which is equal to the number of linear independent rows. This is denoted as rk(M).

Attributes:

  1. rk(M) = rk(M^T)
  2. full rank means rk(M) = min(m, n)

Exercise: Find the rank of following matrix

(1)   \begin{align*}a) M & = \begin{bmatrix}2 & -3 \\6 & -9 \end{bmatrix} \\b) M & = \begin{bmatrix}3 & 1 & 0 \\-6 & -2 & 0\end{bmatrix}\end{align*}

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