Square Roots of Matrices and Operators
If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 = A; we then define A1/2 = √A = B. In general matrices may have multiple square roots or even an infinitude of them. For example the 2×2 identity matrix has an infinity of square roots.
Read more about this topic: Square Root
Famous quotes containing the words square and/or roots:
“After the planet becomes theirs, many millions of years will have to pass before a beetle particularly loved by God, at the end of its calculations will find written on a sheet of paper in letters of fire that energy is equal to the mass multiplied by the square of the velocity of light. The new kings of the world will live tranquilly for a long time, confining themselves to devouring each other and being parasites among each other on a cottage industry scale.”
—Primo Levi (1919–1987)
“Though of erect nature, man is far above the plants. For man’s superior part, his head, is turned toward the superior part of the world, and his inferior part is turned toward the inferior world; and therefore he is perfectly disposed as to the general situation of his body. Plants have the superior part turned towards the lower world, since their roots correspond to the mouth, and their inferior parts towards the upper world.”
—Thomas Aquinas (c. 1225–1274)