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If your matrix is A (doesn't have to be square, can be nxm) and has rank $r< min(n,m)$, then the null space is spanned by ${max(n,m)-r}$ orthogonal vectors and is the space orthogonal to the $span$(A) $\in \mathbb{R}^{max(n,m)}$ (i.e., the linear combination of the basis/orthogonal vectors $\in \mathbb{R}^{max(n,m)}$ that are orthogonal to the $r$ basis vectors of A). In the simplest example, if $A=\left[\begin{array}{cc} 1&0\\ 0&0 \end{array}\right] $, then $span(A)=\alpha\left[\begin{array}{c} 1\\ 0 \end{array}\right], \alpha \in \mathbb{R}$ and $null(A)=\beta\left[\begin{array}{c} 0\\ 1 \end{array}\right], \beta \in \mathbb{R}$

Play around with "null" in base Matlab, or SVD in Python like in this answer

If your matrix is A (doesn't have to be square, can be nxm) and has rank $r< min(n,m)$, then the null space is spanned by ${max(n,m)-r}$ orthogonal vectors and is the space orthogonal to the $span$(A) $\in \mathbb{R}^{max(n,m)}$ (i.e., the linear combination of the basis/orthogonal vectors $\in \mathbb{R}^{max(n,m)}$ that are orthogonal to the $r$ basis vectors of A). See rank-nullity theorem. In the simplest example, if $A=\left[\begin{array}{cc} 1&0\\ 0&0 \end{array}\right] $, then $span(A)=\alpha\left[\begin{array}{c} 1\\ 0 \end{array}\right], \alpha \in \mathbb{R}$ and $null(A)=\beta\left[\begin{array}{c} 0\\ 1 \end{array}\right], \beta \in \mathbb{R}$

Play around with "null" in base Matlab, or SVD in Python like in this answer, where it can be seen that any zero eigenvalues correspond to eigenvectors in the left matrix that span the null space (also see here)

If your matrix is A (doesn't have to be square, can be nxm) and has rank $r< min(n,m)$, then the null space is $\in \mathbb{R}^{max(n,m)}$ spanned by ${max(n,m)-r}$ orthogonal vectors and is the space orthogonal to the $span$(A) $\in \mathbb{R}^{max(n,m)}$ (i.e., the linear combination of the basis/orthogonal vectors that are orthogonal to the r basis vectors of A). In the simplest example, if $A=\left[\begin{array}{cc} 1&0\\ 0&0 \end{array}\right] $, then $span(A)=\alpha\left[\begin{array}{c} 1\\ 0 \end{array}\right], \alpha \in \mathbb{R}$ and $null(A)=\beta\left[\begin{array}{c} 0\\ 1 \end{array}\right], \beta \in \mathbb{R}$

Play around with "null" in base Matlab, or SVD in Python like in this answer

If your matrix is A (doesn't have to be square, can be nxm) and has rank $r< min(n,m)$, then the null space is spanned by ${max(n,m)-r}$ orthogonal vectors and is the space orthogonal to the $span$(A) $\in \mathbb{R}^{max(n,m)}$ (i.e., the linear combination of the basis/orthogonal vectors $\in \mathbb{R}^{max(n,m)}$ that are orthogonal to the $r$ basis vectors of A). In the simplest example, if $A=\left[\begin{array}{cc} 1&0\\ 0&0 \end{array}\right] $, then $span(A)=\alpha\left[\begin{array}{c} 1\\ 0 \end{array}\right], \alpha \in \mathbb{R}$ and $null(A)=\beta\left[\begin{array}{c} 0\\ 1 \end{array}\right], \beta \in \mathbb{R}$

Play around with "null" in base Matlab, or SVD in Python like in this answer

If your matrix is A (doesn't have to be square, can be nxm) and has rank $r< min(n,m)$, then the null space is $\in \mathbb{R}^{min(n,m)-r}$ and is the space orthogonal to the $span$(A) $\in \mathbb{R}^r$ (i.e., the linear combination of the basis/orthogonal vectors that are orthogonal to the basis vectors of A). In the simplest example, if $A=\left[\begin{array}{cc} 1&0\\ 0&0 \end{array}\right] $, then $span(A)=\alpha\left[\begin{array}{c} 1\\ 0 \end{array}\right], \alpha \in \mathbb{R}$ and $null(A)=\beta\left[\begin{array}{c} 0\\ 1 \end{array}\right], \beta \in \mathbb{R}$

Play around with "null" in base Matlab, or SVD in Python like in this answer

If your matrix is A (doesn't have to be square, can be nxm) and has rank $r< min(n,m)$, then the null space is $\in \mathbb{R}^{max(n,m)}$ spanned by ${max(n,m)-r}$ orthogonal vectors and is the space orthogonal to the $span$(A) $\in \mathbb{R}^{max(n,m)}$ (i.e., the linear combination of the basis/orthogonal vectors that are orthogonal to the r basis vectors of A). In the simplest example, if $A=\left[\begin{array}{cc} 1&0\\ 0&0 \end{array}\right] $, then $span(A)=\alpha\left[\begin{array}{c} 1\\ 0 \end{array}\right], \alpha \in \mathbb{R}$ and $null(A)=\beta\left[\begin{array}{c} 0\\ 1 \end{array}\right], \beta \in \mathbb{R}$

Play around with "null" in base Matlab, or SVD in Python like in this answer