Matrix: Difference between revisions

Revision as of 23:48, 12 February 2009

The identity matrix, $I$ , is defined as the matrix that satisfies the condition

$IA=A\!$

For any m-by-n matrix $A$ .

For example the identity matrix in R ³

$\mathbf {I} _{3}={\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}}$

A three diemensional vector

${\overrightarrow {v}}_{3}=v_{1}{\hat {i}}+v_{2}{\hat {j}}+v_{3}{\hat {k}}\!$

has the matrix representation

${\overrightarrow {v}}_{3}={\begin{bmatrix}v_{1}\\v_{2}\\v_{3}\end{bmatrix}}$

Or more generally, an n-diemensional vector has the matrix form

${\overrightarrow {v}}_{n}={\begin{bmatrix}v_{1}\\v_{2}\\\vdots \\v_{n}\end{bmatrix}}$

@@ Line 1: / Line 1: @@
-==Vectors==
+==Basics==
-A vector
+===Identity Matrix===
+The identity matrix, <math>I</math>, is defined as the matrix that satisfies the condition
-<math>\overrightarrow v = v_1\hat i + v_2\hat j + v_3\hat k\!</math>
+<math>IA = A\!</math>
+For any m-by-n matrix <math>A</math>.
+For example the identity matrix in '''R''' <sup>'''3'''</sup>
+<math>\mathbf{I}_3 =
+\begin{bmatrix}
+& 0 & 0 \\
+& 1 & 0 \\
+& 0 & 1
+\end{bmatrix}
+</math>
+===Vectors===
+A three diemensional vector
+<math>\overrightarrow v_3 = v_1\hat i + v_2\hat j + v_3\hat k\!</math>
 has the matrix representation
-<math>\overrightarrow v = \begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix}</math>
+<math>\overrightarrow v_3 = \begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix}</math>
 Or more generally, an n-diemensional vector has the matrix form
-<math>\overrightarrow v = \begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix}</math>
+<math>\overrightarrow v_n = \begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix}</math>
+==Eigenvalue Analysis==