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.
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.
举一反三
- If P is an[img=44x19]1803b6aa96e88c4.png[/img] matrix with orthogonal columns, then[img=72x23]1803b6aa9ec8a8d.png[/img]
- Let [img=99x19]1803c4e7d6c70bb.png[/img] be a linear transformation. If A is the standard matrix representation of [img=13x19]1803c4e7de70caa.png[/img], then an [img=44x19]1803c4e7e5f3add.png[/img] matrix B will also be a matrix representation of L if and only if B is similar to A.
- Let A be a 4×4 matrix, the determinant of A is 1/3, and [img=21x20]1803c4e4937ebc3.png[/img] the adjoint matrix of A, then [img=115x27]1803c4e49b725a2.png[/img]=________. A: 1 B: 3 C: 6 D: 9
- 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.
- 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.