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orthogonality condition
An orthogonality condition is a mathematical constraint requiring that a set of vectors, or the column vectors of a matrix, be mutually perpendicular, meaning their inner products are equal to zero. In matrix notation, this is typically formulated by enforcing that the product of a matrix and its transpose yields an identity or diagonal matrix. Within matrix factorization, dimensionality reduction, and clustering algorithms, imposing an orthogonality condition ensures that derived factor matrices and latent components share no overlapping variance. This requirement eliminates redundancy, promotes uniqueness and stability in matrix decompositions, and allows the resulting factor components to be directly interpreted as distinct, non-overlapping cluster indicators or independent basis directions.
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