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iamzzz
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Why is that Nullspace of A is subset of nullspace of A^T*A
let's say that A is m*n matrix
let's say that A is m*n matrix
Why is that Nullspace of A is subset of nullspace of A^T*A
- Context: Undergrad
- Thread starter iamzzz
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SUMMARY
The discussion clarifies that the null space of matrix A is indeed a subset of the null space of the product A^T*A. Given an m*n matrix A, if X is in the null space of A (AX=0), then it follows that A^T*AX equals zero, confirming that X is also in the null space of A^T*A. This relationship holds true, although X may not encompass the entire null space of A^T.
PREREQUISITES- Understanding of linear algebra concepts, specifically null spaces.
- Familiarity with matrix multiplication and transpose operations.
- Knowledge of the properties of linear transformations.
- Basic proficiency in mathematical notation and terminology.
- Study the properties of null spaces in linear algebra.
- Explore the implications of the Rank-Nullity Theorem.
- Learn about the relationship between null spaces and linear transformations.
- Investigate applications of A^T*A in least squares problems.
Students and professionals in mathematics, particularly those studying linear algebra, as well as data scientists and engineers working with matrix computations.
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