The image singular value vector has invariance about the transformation of translation, rotation, etc. It is considered as a kind of image algebraic character, applied in image matching and image recognition widely. By matrix operation, the invariance of image singular value vector about the reducing and enlarging transformation is proved, and this character is applied to the image matching. The experimental results show this invariance is an important character of the image singular value vector as same as other invariance about the translation and rotation transformation.