For Kronecker product query oracles, trace and spectral norm estimation require exponentially many queries for all well-conditioned algorithms, and {±1} probe alphabets make zero-testing exponentially weaker than Gaussian probes.
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Understanding the Kronecker Matrix-Vector Complexity of Linear Algebra
For Kronecker product query oracles, trace and spectral norm estimation require exponentially many queries for all well-conditioned algorithms, and {±1} probe alphabets make zero-testing exponentially weaker than Gaussian probes.