Two methods for color constancy are proposed in this paper. Both are based on the correlation matrix on the three-dimensional space of colors, red, green and blue. In the first method, the eigenvector corresponding to the largest eigenvalue is assumed to be a good estimate of the illumination color, and the influence of the illumination color is eliminated from the input image. In the second method, it is assumed that the eigenvector corresponding to the largest eigenvalue presents the color gray when the illumination is white The image under white illumination is obtained by a iteration method so as to satisfy the condition that the eigenvector corresponding to the largest eigenvalue presents the color gray. These two methods were compared to a widely used typical method for color constancy, the Gray-world method, by simulation experiments using synthesized images and real images, and the effectiveness of the proposed methods was validated by these experiments.