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In-place linear transformations allow input to be overwritten with the output of the transformation. This paper presents a family of in-place linear transformations based on block lower/upper (LU) decompositions, of which the known transformation via LU decomposition is a special case, and shows that the proposed family includes a class of transformations that possesses the cache-oblivious property. Furthermore, the number of cache misses and approaches for non-square matrices is discussed. The simulation shows that the proposed in-place linear transformation is faster than the existing transformation via LU decompositions.