We show, step-by-step, how to find a basis and matrix that gives a diagonalized matrix representation of the linear transformation.

# Category: Linear Algebra

## Standard Matrix of a Transformation

We show, step-by-step, how to find the standard matrix for a given linear transformation.

## Kernel and Range

We show, step-by-step, how to find the kernel, range, rank and nullity of a linear transformation defined by matrix multiplication.

## Orthogonal Complement

We show, step-by-step, how to find the orthogonal complement of a given vector space.

## Gram-Schmidt Orthonormalization

We show, step-by-step, how to find an orthonormal basis for a given vector space by using the Gram-Schmidt orthonormalization process.