Transpose of a Matrix

Example: Find Transpose

Given

Properties of Transpose

Example: Verify (AB)ᵀ = BᵀAᵀ

Let and .

Applications

The transpose is used in:

1. Defining symmetric and skew-symmetric matrices
2. Computing and (used in least squares)
3. Orthogonal matrices:

Example: Verify Orthogonal

Check if is orthogonal.