LEC17

Outline

• $A_{m\times n}$ is a matrix with $m$ rows and $n$ columns.
• Matrices are equal if each of their corresponding entries are equal.
• If $m=n$, we have a square matrix.
• Addition of matrices: just like vectors, corresponding entries are summed up.
• Scalar multiplication of matrices: like vectors, each entry is multiplied with the scalar multiple.
• Transpose of $A_{m\times n}$ is $A_{n\times m}^T$. Rows become columns, and cols become rows.
  • $(A^T{)}^T=A$
  • $(A+B{)}^T=A^T+B^T$
  • $(cA{)}^T=c{A}^T$
• Symmetric matrices. If $A^T=A⟹n=m$. (not vice versa)