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Matrix Algebra

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Overview

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This course introduces matrix algebra through matrix multiplication, inverses, elementary matrices, LU factorization, outer products, and rank. It also develops foundational concepts involving subspaces, nullspaces, bases, dimensions, and coordinates.

Syllabus

Matrix Multiplication.
ABBA.
Inverse of matrix.
Invertible matrix.
Invertible matrices are square.
Elementary Matrix.
Product of elementary matrices.
LU factorization.
Subspace.
Not subspace.
Span is a subspace.
Nullspace of a matrix.
Nullspace is a subspace.
Basis and dimension.
Check something is a basis.
Coordinates.
Nullspace Column Space and Rank.
Infinite dimensions.
Outer Product.
Magic Matrix.

Taught by

Dr Peyam

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