(New page: ='''1.13 etc.'''= Inner product space Any Euclidean space <math>\mathbf{R}^{n}</math> with dot product is an inner product space. <math>\left\langle \left(x_{1},\cdots,x_{n}\right),\le...) |
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='''1.13 etc.'''= | ='''1.13 etc.'''= | ||
| − | + | From the [[ECE_600_Prerequisites|ECE600 Pre-requisites notes]] of [[user:han84|Sangchun Han]], [[ECE]] PhD student. | |
| + | ---- | ||
Inner product space | Inner product space | ||
| − | Any Euclidean space <math>\mathbf{R}^{n}</math> with dot product is an inner product space. | + | Any Euclidean space <math class="inline">\mathbf{R}^{n}</math> with dot product is an inner product space. |
<math>\left\langle \left(x_{1},\cdots,x_{n}\right),\left(y_{1},\cdots,y_{n}\right)\right\rangle \triangleq\sum_{i=1}^{n}x_{i}y_{i}</math> | <math>\left\langle \left(x_{1},\cdots,x_{n}\right),\left(y_{1},\cdots,y_{n}\right)\right\rangle \triangleq\sum_{i=1}^{n}x_{i}y_{i}</math> | ||
| + | |||
| + | ---- | ||
| + | [[ECE600|Back to ECE600]] | ||
| + | |||
| + | [[ECE 600 Prerequisites|Back to ECE 600 Prerequisites]] | ||
Latest revision as of 10:34, 30 November 2010
1.13 etc.
From the ECE600 Pre-requisites notes of Sangchun Han, ECE PhD student.
Inner product space
Any Euclidean space $ \mathbf{R}^{n} $ with dot product is an inner product space.
$ \left\langle \left(x_{1},\cdots,x_{n}\right),\left(y_{1},\cdots,y_{n}\right)\right\rangle \triangleq\sum_{i=1}^{n}x_{i}y_{i} $
