Example · High school
Terms
| Term | This example | Why |
|---|
| array rank |
$2$
|
The identity matrix has two axes, so its number of axes is $2$. Its rank as a matrix is $3$, because its $3$ columns are linearly independent.
|
| shape |
$(3, 3)$
|
|
| array size |
$3 \cdot 3 = 9$
|
|
| matrix rank |
$\operatorname{rank} I = 3$
|
The $3 \times 3$ identity matrix has rank $3$, because its columns are linearly independent.
|
| positive definite matrix |
✓ |
The $3 \times 3$ identity matrix is positive definite, because $x^{\top} I x = \norm{x}^2 > 0$ for every nonzero $x$.
|
| positive semidefinite |
✓ |
The $3 \times 3$ identity matrix is positive semidefinite, because it is positive definite.
|
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