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Remark:A nonempty collection A of matrices is called an algebra (of matrices) if A is closed under the operations of matrix addition, scalar multiplication, and matrix multiplication. Clearly, the square matrices with a given order form an algebra of matrices, but so do the scalar, diagonal, ...
High-quality numerical linear algebra software usually works with Rx = Q^Tb instead of the normal equations in order to reduce the accumulation of rounding errors made during computer arithmetic.Further Reading: Textbook, Chapter 4.4.Lecture 19 (April 3)...
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