Transformation matrix: We consider the vector space, in which we define the line

Question

Transformation matrix: We consider the vector space, in which we define the line y = ax, where a is a given positive coefficient. Show (using a diagram) that function that takes a vector and project it (orthogonally) on the line is indeed a linear map Compute the matrix of this linear map A Using Matlab, compute the projections of the vectors (2, 1), (-1, 0), (4, 3), (-0.5, 1), (3, -2.5) on the line L y=ax, with a = 0.2, using the matrix A that you defined above Using the scatter function (in Matlab), plot the vectors defined above and their projections on the line L

Explanation / Answer

lbu $10, matrix
lbu $11, matrix+1
lbu $12, matrix+2
lbu $13, matrix+3
lbu $14, matrix+4
lbu $15, matrix+5
lbu $16, matrix+6
lbu $17, matrix+7
lbu $18, matrix+8
lbu $19, matrix+9
lbu $20, matrix+10
lbu $21, matrix+11
lbu $22, matrix+12
lbu $23, matrix+13
lbu $24, matrix+14
lbu $25, matrix+15

addiu $2, $0, 8
addiu $9, $0, 256
loop:
addiu $2, $2, -1
srl $9, $9, 1
addu $27, $0, $0

and $26, $10, $9
srlv $26, $26, $2
or $27, $27, $26

and $26, $11, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $12, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $13, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $14, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $15, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $16, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $17, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $18, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $19, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $20, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $21, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $22, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $23, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $24, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

and $26, $25, $9
srlv $26, $26, $2
sll $27, $27, 1
or $27, $27, $26

sll $3, $2, 1
sh $27, transposed($3)
bgez $2, loop
nop

.data 0x2000
matrix:
.byte 0x80
.byte 0x80
.byte 0x40
.byte 0x40
.byte 0x20
.byte 0x20
.byte 0x10
.byte 0x10
.byte 0x08
.byte 0x08
.byte 0x04
.byte 0x04
.byte 0x02
.byte 0x02
.byte 0x01
.byte 0x01

.data 0x3000
transposed:
.half 0
.half 0
.half 0
.half 0
.half 0
.half 0
.half 0
.half 0

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