MATLAB Function Reference
qrdelete

Delete column or row from QR factorization

Syntax

• ```[Q1,R1] = qrdelete(Q,R,j)
[Q1,R1] = qrdelete(Q,R,j,'col')
[Q1,R1] = qrdelete(Q,R,j,'row')
```

Description

```[Q1,R1] = qrdelete(Q,R,j) ``` returns the QR factorization of the matrix `A1`, where `A1` is `A` with the column `A(:,j)` removed and `[Q,R] = qr(A)` is the QR factorization of `A`.

```[Q1,R1] = qrdelete(Q,R,j,'col') ``` is the same as `qrdelete(Q,R,j)`.

```[Q1,R1] = qrdelete(Q,R,j,'row') ``` returns the QR factorization of the matrix `A1`, where `A1` is `A` with the row `A(j,:)` removed and `[Q,R] = qr(A)` is the QR factorization of `A`.

Examples

• ```A = magic(5);
[Q,R] = qr(A);
j = 3;
[Q1,R1] = qrdelete(Q,R,j,'row');

Q1 =
0.5274   -0.5197   -0.6697   -0.0578
0.7135    0.6911    0.0158    0.1142
0.3102   -0.1982    0.4675   -0.8037
0.3413   -0.4616    0.5768    0.5811

R1 =
32.2335   26.0908   19.9482   21.4063   23.3297
0  -19.7045  -10.9891    0.4318   -1.4873
0         0   22.7444    5.8357   -3.1977
0         0         0  -14.5784    3.7796
```

returns a valid QR factorization, although possibly different from

• ```A2 = A;
A2(j,:) = [];
[Q2,R2] = qr(A2)

Q2 =
-0.5274    0.5197    0.6697   -0.0578
-0.7135   -0.6911   -0.0158    0.1142
-0.3102    0.1982   -0.4675   -0.8037
-0.3413    0.4616   -0.5768    0.5811

R2 =
-32.2335  -26.0908  -19.9482  -21.4063  -23.3297
0   19.7045   10.9891   -0.4318    1.4873
0         0  -22.7444   -5.8357    3.1977
0         0         0  -14.5784    3.7796
```

Algorithm

The `qrdelete` function uses a series of Givens rotations to zero out the appropriate elements of the factorization.

`planerot`, `qr`, `qrinsert`