TSSFL TECHNOLOGY STACK

Advanced Linear Algebra

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Below is a series of lectures in Linear Algebra, presented by Gilbert Strang from MIT:

Suppose that A and B are invertible matrices such that multiplication operation is possible on the two matrices, then AB is invertible.

Here is the...

If A is a non-zero n\times n matrix and its inverse exists, then such inverse is unique.

Proof

Suppose that a matrix A has two inverses B and C...

Example: Apply the Gram-Schmidt process to find an orthonormal matrix P that diagonalizes

A = \begin{bmatrix}0&2&2 \\ 2&0&2\\ 2&2&0 \end{bmatrix}...

Example: Apply elementary row operations to find the inverse of the matrix \

Solution

Apply successively elementary row operations

r_1 + r_2...