Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
linear_algebra:01_matrices [2014/01/20 12:28]
marje
linear_algebra:01_matrices [2014/12/14 00:03] (current)
jaan fixed spelling typos
Line 82: Line 82:
 <​BOOKMARK:​m_multiplication>​ <​BOOKMARK:​m_multiplication>​
  
-^Operaton ​^Formular ​^Example^+^Operation ​^Formula ​^Example^
 | Sum | $(a_{ij})+(b_{ij})=(a_{ij}+b_{ij})$ | $\begin{pmatrix}\color{blue}{1} & \color{blue}2\\\color{blue}0 &​\color{blue}{-2}\end{pmatrix}+\begin{pmatrix}\color{red}{0} &​\color{red}{-1}\\\color{red}1 & \color{red}2\end{pmatrix}=\begin{pmatrix}\color{blue}1+\color{red}0 & \color{blue}2+\color{red}{(-1)}\\\color{blue}0+\color{red}1 & \color{blue}{-2}+\color{red}2\end{pmatrix}=\begin{pmatrix}1 & 1\\1 & 0 \end{pmatrix}$ | | Sum | $(a_{ij})+(b_{ij})=(a_{ij}+b_{ij})$ | $\begin{pmatrix}\color{blue}{1} & \color{blue}2\\\color{blue}0 &​\color{blue}{-2}\end{pmatrix}+\begin{pmatrix}\color{red}{0} &​\color{red}{-1}\\\color{red}1 & \color{red}2\end{pmatrix}=\begin{pmatrix}\color{blue}1+\color{red}0 & \color{blue}2+\color{red}{(-1)}\\\color{blue}0+\color{red}1 & \color{blue}{-2}+\color{red}2\end{pmatrix}=\begin{pmatrix}1 & 1\\1 & 0 \end{pmatrix}$ |
 | Scalar multiplication | $c\cdot (a_{ij})=(c\cdot a_{ij})$ | $\color{blue}{-1}\cdot\begin{pmatrix}1 & 8 \\5 &-2 \end{pmatrix}=$ $\begin{pmatrix}\color{blue}{-1}\cdot 1 & \color{blue}{-1}\cdot 8 \\\color{blue}{-1}\cdot 5 &​\color{blue}{-1}\cdot (-2)\end{pmatrix}=\begin{pmatrix}-1 & -8 \\-5 &  2 \end{pmatrix}$| | Scalar multiplication | $c\cdot (a_{ij})=(c\cdot a_{ij})$ | $\color{blue}{-1}\cdot\begin{pmatrix}1 & 8 \\5 &-2 \end{pmatrix}=$ $\begin{pmatrix}\color{blue}{-1}\cdot 1 & \color{blue}{-1}\cdot 8 \\\color{blue}{-1}\cdot 5 &​\color{blue}{-1}\cdot (-2)\end{pmatrix}=\begin{pmatrix}-1 & -8 \\-5 &  2 \end{pmatrix}$|
Line 174: Line 174:
 Another important operation on matrices is that of taking **the transpose**. It is denoted by placing a $T$ as an exponent on the initial matrix. Another important operation on matrices is that of taking **the transpose**. It is denoted by placing a $T$ as an exponent on the initial matrix.
  
-^Operaton ​^Formular ​^Example^+^Operation ​^Formula ​^Example^
 | Transpose |$(a_{ij})^T=(a_{ji})$ | $\begin{pmatrix}\color{blue}1 & \color{blue}2 & \color{blue}{-6}\\ \color{red}3 & \color{red}5 & \color{red}4\end{pmatrix}^T=\begin{pmatrix}\color{blue}1 & \color{red}3\\ \color{blue}2 & \color{red}5\\ \color{blue}{-6} & \color{red}4\end{pmatrix}$ | | Transpose |$(a_{ij})^T=(a_{ji})$ | $\begin{pmatrix}\color{blue}1 & \color{blue}2 & \color{blue}{-6}\\ \color{red}3 & \color{red}5 & \color{red}4\end{pmatrix}^T=\begin{pmatrix}\color{blue}1 & \color{red}3\\ \color{blue}2 & \color{red}5\\ \color{blue}{-6} & \color{red}4\end{pmatrix}$ |
  
linear_algebra/01_matrices.txt ยท Last modified: 2014/12/14 00:03 by jaan