#Type/Theorem #Topic/Linear_Algebra

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 9.13 Transpose of a Matrix

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Algebraic Properties of Matrix Transposes

Let matrices A,B∈Rm×n and c∈R. Then, all of the following are properties of matrix transposes:

  1. Two Transposes ((A)T)T=A
  2. Transpose of a Sum: (A+B)T=AT+BT
  3. Scalars come out of Transposes: (cA)T=cAT
  4. Transpose of a Matrix Product: (A⋅B)T=BT⋅AT