A matrix is a set of numbers arranged in a rectangular array. The array of numbers is divided in rows and columns. The matrix size determines the scan resolution.

The matrix size is the number of data points collected in one, two or three directions. Normally used for the 2D in plane sampling. The display matrix may be different from the acquisition matrix, although the latter determines the resolution.

The elements of a rectangular array transducer (also called matrix transducer) are arranged in a rectangular pattern. Rectangular arrays with unequal rows (e.g. 3, 5, 7) of transducer elements are in real 2D (two-dimensional), but they are termed 1.5D, because the number of rows is much less than the number of columns. Their main advantage is electronic focusing even in the elevation plane (z-plane).
The transducers that are termed 2D have an equal number of rows and columns. 2D transducers have the potential to provide real-time 3D ultrasound imaging without moving the transducer.
Active matrix array transducers have several elements in the short axis and in addition multiple elements along the long axis. This allows electronic focusing in both axes, resulting in a narrower elevation axis beam width in the near field and far field.

The earliest introduction of vascular ultrasound contrast agents (USCA) was by Gramiak and Shah in 1968, when they injected agitated saline into the ascending aorta and cardiac chambers during echocardiographic to opacify the left heart chamber. Strong echoes were produced within the heart, due to the acoustic mismatch between free air microbubbles in the saline and the surrounding blood.

Linear array transducer elements are rectangular and arranged in a line. Linear array probes are described by the radius of width in mm. A linear array transducer can have up to 512 elements spaced over 75-120 mm. The beam produced by such a narrow element will diverge rapidly after the wave travels only a few millimeters. The smaller the face of the transducer, the more divergent is the beam. This would result in poor lateral resolution due to beam divergence and low sensitivity due to the small element size.
In order to overcome this, adjacent elements are pulsed simultaneously (typically 8 to 16; or more in wide-aperture designs). In a subgroup of x elements, the inner elements pulse delayed with respect to the outer elements. The interference of the x small divergent wavelets produces a focused beam. The delay time determines the depth of focus for the transmitted beam and can be changed during scanning.
Linear arrays are usually cheaper than sector scanners but have greater skin contact and therefore make it difficult to reach organs between ribs such as the heart. One-dimensional linear array transducers may have dynamic, electronic focusing providing a narrow ultrasound beam in the image plane. In the z-plane (elevation plane - perpendicular to the image plane) focusing may be provided by an acoustic lens with a fixed focal zone.
Rectangular or matrix transducers with unequal rows of transducer elements are two-dimensional (2D), but they are termed 1.5D, because the number of rows is much less than the number of columns. These transducers provide dynamic, electronic focusing even in the z-plane.

See also Rectangular Array Transducer.