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

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# Tag: linear algebra

Blogs, Linear Algebra## Diagonalized Matrix

Blogs, Linear Algebra## Standard Matrix of a Transformation

Blogs, Linear Algebra## Kernel and Range

Blogs, Linear Algebra## Orthogonal Complement

Blogs, Linear Algebra## Gram-Schmidt Orthonormalization

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

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

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

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

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