# Example Fixed Sized Matrices

Array access adds a significant amount of overhead to matrix operations. A fixed sized matrix gets around that issue by having each element in the matrix be a variable in the class. EJML provides support for fixed sized matrices and vectors up to 6x6, at which point it loses its advantage. The example below demonstrates how to use a fixed sized matrix and convert to other matrix types in EJML.

External Resources:

## Example

```/**
* In some applications a small fixed sized matrix can speed things up a lot, e.g. 8 times faster.  One application
* which uses small matrices is graphics and rigid body motion, which extensively uses 3x3 and 4x4 matrices.  This
* example is to show some examples of how you can use a fixed sized matrix.
*
* @author Peter Abeles
*/
public class ExampleFixedSizedMatrix {
public static void main( String[] args ) {
// declare the matrix
DMatrix3x3 a = new DMatrix3x3();
DMatrix3x3 b = new DMatrix3x3();

// Can assign values the usual way
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
a.set(i, j, i + j + 1);
}
}

// Direct manipulation of each value is the fastest way to assign/read values
a.a11 = 12;
a.a23 = 64;

// can print the usual way too
a.print();

// most of the standard operations are support
CommonOps_DDF3.transpose(a, b);
b.print();

System.out.println("Determinant = " + CommonOps_DDF3.det(a));

// matrix-vector operations are also supported
// Constructors for vectors and matrices can be used to initialize its value
DMatrix3 v = new DMatrix3(1, 2, 3);
DMatrix3 result = new DMatrix3();

CommonOps_DDF3.mult(a, v, result);

// Conversion into DMatrixRMaj can also be done
DMatrixRMaj dm = DConvertMatrixStruct.convert(a, null);

dm.print();

// This can be useful if you need do more advanced operations
SimpleMatrix sv = SimpleMatrix.wrap(dm).svd().getV();

// can then convert it back into a fixed matrix
DMatrix3x3 fv = DConvertMatrixStruct.convert(sv.getDDRM(), (DMatrix3x3)null);

System.out.println("Original simple matrix and converted fixed matrix");
sv.print();
fv.print();
}
}
```