## Department of Mathematics

Indian Institute Of Technology Madras , Chennai
• Office of the Department of Mathematics is moved from HSB to New Academic Complex (NAC) 5th and 6th Floor

### Spectral Theorem-I

#### Abstract :

The Spectral theorem establishes conditions under which an operator can be expressed in a simple form ( sum of “simpler” operators). This talk is divided into two parts. In the first talk, we will discuss the spectral theorem in a finite dimensional complex Hilbert space. In a finite dimensional space, the spectral theorem says that a normal linear operator/matrix is unitary equivalent to diagonal operator/matrix (here diagonal matrices are the “simpler” matrices). We will see one important application of the spectral theorem, namely the idea of defining a functional calculus. In the second talk, we will do the same on an infinite dimensional Hilbert space.

Key Speaker Repana Devendra, Research Scholar, Department of Mathematics, IITM
Place NAC 519
Start Time 3:00 PM
Finish Time 4:00 PM