# Category:Pairwise Orthogonality

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This category contains results about **Pairwise Orthogonality**.

Definitions specific to this category can be found in Definitions/Pairwise Orthogonality.

Let $\sqbrk a_{m n}$ be a matrix of order $m \times n$.

### Rows

The rows of $\sqbrk a_{m n}$ are described as **pairwise orthogonal** if and only if:

- $\forall i, j \in \set {1, 2, \ldots, m}, i \ne j: {r_i}^\intercal \cdot {r_j}^\intercal = 0$

That is, the dot product of each pair of distinct rows of $\sqbrk a_{m n}$, when transposed and considered as vectors, is zero.

### Columns

The columns of $\sqbrk a_{m n}$ are described as **pairwise orthogonal** if and only if:

- $\forall i, j \in \set {1, 2, \ldots, n}, i \ne j: c_i \cdot c_j = 0$

That is, the dot product of each pair of distinct columns of $\sqbrk a_{m n}$, when considered as vectors, is zero.

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