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Insights into Mathematics via YouTube
CONTENT SUMMARY: pg 1: @ Lesson about nullity and rank of a linear transformation; kernel and image of linear transformation; general linear transformations; Example mxn is 3x4;
pg 2: @ How to visualize in higher dimensions; shift from affine space to vector space; points/vectors;
pg 3: @ 4-dimensional space algebraically;
pg 4: @ 4-dimensional space geometrically;
pg 5: @ linear transformation from 4dim to 3dim; Kernel and image of transformation as fundamental; nullity as dimension of the kernel; rank as dimension of the image;
pg 6: @ Definition of kernel vector; kernel property;
pg 7: @ Finding vectors with the kernel property for a transformation using row reduction;
pg 8: @28:32 Definition of image vector; image property; pg 9: @ at least the columns of the transformation matrix have this image property;
pg 10: @ Finding vectors with the image property for a transformation using row reduction;
pg 11: @ Another approach to the image of a transformation; the column space of a matrix;
pg 12: @ The whole picture; kernel,image, nullity, rank;
pg 13: @ Important observations;
pg 14: @ relationship between the nullity and the rank; Rank-Nullity theorem;
pg 15: @ example: Linear transformation from 3dim space to 4dim space; kernel, image, rank, nullity;
pg 16: @ example continued; kernel;
pg 17: @52:43 example continued; image; remark on relationship of columns in row reduction @;
pg 18: @ example summary;
pg 19: @ exercises 17.1:2; kernel property, image property;
pg 20: @ exercise 17.3 ; describe ker and im; THANKS to EmptySpaceEnterprise
Insights into Mathematics
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