Transpose

Matrix obtained from a given matrix by interchanging its rows and columns. Denoted with a superscript T, like $A^T$. $$

Properties

• $(A^T)^T=A$
• Distributive over addition: $(A+B)^T=A^T+B^T$
• $(kA)^T=kA^T$
• $(A\times B)^T=B^T\times A^T$
• Spectrum of $A^T$ is equal to the spectrum of $A$
• $\big|A^{T}\big|=|A|$