MatrixNotes11810

MatrixNotes11810 - Discussion Section Notes - Matrices...

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Discussion Section Notes - Matrices Everything You Need to Know About Matrices Conceptually matrices are an extension of one-dimensional math 1-dimensional n-dimensional values scalar vector mapping effect(s) of multiplication stretch/compress, flip stretch/compress, flip multiplication condition to reduce dimension 0 (to a single point) determinant=0 (singular matrix, maps to a line or single point) multiplication commutes yes no multiplicative inverse yes (if x <> 0) yes (if det <> 0) Types of Matrices, Matrix Properties diagonal index determinant trace positive, non-negative primitive Determinants real number, not a matrix (can be < 0) can only take the determinant of a square matrix if det = 0 the matrix doesn’t have an multiplicative inverse determinant of a 2x2 matrix: ad – bc taking the determinant of a 3 x 3 matrix (see http://www.richland.cc.il.us/james/lecture/m116/matrices/determinant.html ) Finding the Inverse question: can a non-square matrix have an inverse? minor for a specific element in a matrix: the determinant of the matrix that results when you eliminate the row and column of that element cofactor of the element in row r column j: (–1) r+j x the minor for that element. In other words cofactor is determinant of the matrix that results when you eliminate row r and column j,
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MatrixNotes11810 - Discussion Section Notes - Matrices...

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