backends/default Design

Responsibilities

• Present immut and mutable as default dense backends through owned wrapper types.
• Implement capability traits for the default dense matrix and vector types.
• Provide small generic helpers that exercise trait-based dispatch.

Non-Responsibilities

• Do not redefine scalar algebra or arithmetic laws.
• Do not require all future backends to become dense or contiguous.
• Do not make scalar-valued maps part of the core linear algebra trait surface.

Extension Model

Future sparse, lazy, static-size, GPU, or external-library backends should implement the same structural traits directly. They should not need to convert into DenseMatrix or DenseVector before generic algorithms can use them.