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peterlam
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For a matrix A, if its nullity is equal to 1, what is the implication of that? What spans its null space?
Thanks a lot!
Thanks a lot!
The nullity of a matrix is the dimension of its null space, which is the set of all vectors that, when multiplied by the matrix, result in a zero vector. In other words, it is the number of linearly independent columns in the matrix that can be combined to produce a zero vector.
The nullity of a matrix is equal to the number of columns minus its rank. This is because the rank of a matrix is the number of linearly independent columns, and the nullity is the number of linearly dependent columns.
If a matrix has a nullity greater than zero, it means that there are infinitely many solutions to the equation Ax=0, where A is the matrix and x is a vector. This can have practical implications in applications such as solving systems of linear equations or finding the basis of a vector space.
The null space span of a matrix can be determined by finding the null space of the matrix, which is the set of all vectors that, when multiplied by the matrix, result in a zero vector. These vectors can then be combined to form a basis for the null space, which is the null space span.
Yes, a matrix can have a nullity of zero. This means that the null space of the matrix is empty, and there are no linearly independent columns in the matrix that can be combined to produce a zero vector. In other words, the matrix has a full rank and no linearly dependent columns.