Change of Basis. Row and Column Pictures for a Linear System

Change of basis is among the most confusing topics for beginners. From early age, students learn to place coordinate axis in a standard position, so that they perceive any alternative coordinate system as unnatural. A distinct feature of the applet is that the viewer's frame can be modified on the fly. This should help people to realize that there are no such things as "absolute coordinates" in Linear Algebra. We can choose any basis and then visualize position it in any way we like; all other vectors will follow. This also helps to better understand the relation between various interpretations of systems of linear equations, such as the "column" and "row" pictures (in terminology of the G. Strang's textbook).

 

Eugene Yablonski

 
Resource Type
Activity
Tags
2d-vectors  basis  change  combination  coordinates  linear  of  practice  vectors 
Target Group (Age)
18 – 19+
Language
English
 
 
 
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