Let V be a vector space over R. Show that if T is a linear operator on V, the following conditions are equivalent 1. T2 = IV, where IV is the identity in V 2. V is the direct sum of the kernel of (T - IV) and the kernel of (T + IV). 3. There are W and X subspaces of V such that V = W ⊕ X and T (w + x) = w - x, for all w ∈ W, x ∈ X

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.