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If the columns of a transformation matrix are linearly dependent, it means the transformation collapses the space into a lower dimension. For example, a 2D plane might be squashed into a 1D line or a single point.

Conditions: The matrix represents a linear transformation.; Columns are linearly dependent.

YouTubeLinear transformations and matrices | Chapter 3, Essence of linear algebra

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Answers for “矩阵与线性变换有什么关系？”

What does it mean if the columns of a transformation matrix are linearly dependent?+