Change of Basis, Coordinate Vectors, Mapping, Transition Matrix - Linear Algebra

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Science Education change of basis change of basis matrix linear algebra change of basis linear algebra change of coordinates linear algebra change of basis linear algebra examples transition matrix change of basis linear transformation linear algebra coordinate mapping

What is the meaning and purpose of change of basis and why it is useful using an example, defining it as a linear transformation using matrix notation. Coordinate vectors (including unit vectors) relative to a basis are defined, and also the transition matrix formula.

0:00 Coordinate vectors, mapping to R^n
2:13 Change of basis
9:24 Transition matrix
16:32 Calculating the transition matrix between bases for R^n

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