Invertible Transformations

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Description: Corresponding to our algebraic notion of invertibility, we want a geometric notion. Invertible transformations are defined, and then proven to be equivalent (thank goodness!) to invertible matrices when linear.

Learning Objectives:
1) Define an invertible transformation
2) Demonstrate a transformation is invertible by analyzing it's matrix, and vice versa.

This video is part of a Linear Algebra course taught at the University of Cincinnati.

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Комментарии
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This is the best explanation of invertible transformations,

thatPailGuy
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Thank you so much! This is a wonderful explanation.

jingyiwang
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What if the linear transformation is not represented by a square matrix? For example F(x, y) from R2 to R3 defined by F(x, y)=(y, x, y) does not have a square matrix, but it is certainly invertible. The inverse matrix isn't square, and isn't the inverse of the original matrix either. This is bothering me right now, because I thought that only one to one and onto transformations could have an inverse.

austinpundit