Which of the following statement is false?
A: Ais an[img=49x19]1803b6abf33899a.png[/img]matrix.[img=66x23]1803b6abfb9f77f.png[/img]is a QR factorization ofA. The columns ofQform an orthonormal basis for the column space ofA.
B: If A=QR, where Q has orthonormal columns, then[img=79x27]1803b6ac036f846.png[/img]
C: Ahas a QR factorization, then A must be a square matrix.
D: Any matrix can have a QR factorization.
E: If a matrix A has a QR factorization, then the ranks of A and Q are the same.
A: Ais an[img=49x19]1803b6abf33899a.png[/img]matrix.[img=66x23]1803b6abfb9f77f.png[/img]is a QR factorization ofA. The columns ofQform an orthonormal basis for the column space ofA.
B: If A=QR, where Q has orthonormal columns, then[img=79x27]1803b6ac036f846.png[/img]
C: Ahas a QR factorization, then A must be a square matrix.
D: Any matrix can have a QR factorization.
E: If a matrix A has a QR factorization, then the ranks of A and Q are the same.
举一反三
- An[img=49x19]1803b6aafbee947.png[/img] matrix A has orthonormal columns if and only if[img=59x23]1803b6ab03fb852.png[/img].
- Which of the following statement is false? A: If[img=77x23]1803b6aa763b00a.png[/img], where[img=77x23]1803b6aa7e8aab9.png[/img] and D is a diagonal matrix, then B is a symmetric matrix. B: An orthogonal matrix is orthogonally diagonalizable. C: An[img=44x19]1803b6aa8680eb5.png[/img]symmetric matrix has n real eigenvalues. D: An[img=44x19]1803b6aa8680eb5.png[/img]symmetric matrix hasnlinearly independent eigenvectors.
- The columns of the standard matrix for a linear transformation from [img=22x19]1803b6a8c19a71a.png[/img]to [img=25x19]1803b6a8c9f3863.png[/img] are the images of the columns of the [img=44x19]1803b6a8d3fc1b1.png[/img] indentity matrix.
- The columns of any [img=40x20]1803b6a907d8a6a.png[/img] matrix are linearly dependent.
- If P is an[img=44x19]1803b6aa96e88c4.png[/img] matrix with orthogonal columns, then[img=72x23]1803b6aa9ec8a8d.png[/img]