14-240/Tutorial-November11: Difference between revisions
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Recall: |
Recall: |
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Let <math>V</math> be a finite dimensional vector space over a field <math>F</math> |
Let <math>V</math> be a finite dimensional vector space over a field <math>F</math>, <math>B = {v_1, v_2, v_3, ..., v_n}</math> be an ordered basis of <math>V</math> and <math>v \in V</math>. Then <math>v = \displaystyle\sum_{i=1}^{n} c_iv_i</math> where <math>c_i \in F</math>. Then the '''coordinate representation''' of <math>v</math> is the column vector \begin{pmatrix}c_1\\c_2\\c_3\\.\\c_n\end{pmatrix}</math>. |
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Let <math>W</math> be a finite dimensional vector space over the same field <math>F</math>, <math>B = {v_1, v_2, v_3, ..., v_m}</math> be an ordered basis of <math>W</math>. Define a linear transformation <math>T:V \to W</math>. Then the matrix representation of <math>T</math> in the ordered bases <math>B, K</math> is the matrix |
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Revision as of 19:42, 29 November 2014
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Boris
Coordinate and Matrix Representation Problems
Recall:
Let be a finite dimensional vector space over a field , be an ordered basis of and . Then where . Then the coordinate representation of is the column vector \begin{pmatrix}c_1\\c_2\\c_3\\.\\c_n\end{pmatrix}</math>.
Let be a finite dimensional vector space over the same field , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B = {v_1, v_2, v_3, ..., v_m}} be an ordered basis of . Define a linear transformation . Then the matrix representation of in the ordered bases is the matrix
