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Jun 10, 2026 · Fundamentals

Why a Mathematically Free Matrix Transpose Is 10× Slower on CPUs

A naive 1024×1024 matrix transpose can be ten times slower than an optimized version because the CPU sees memory as a linear address space, and row‑major layout combined with cache‑line granularity makes column‑wise accesses incur massive cache misses, which can be eliminated with blocking, prefetching and SIMD techniques.